Artículos de revistas sobre el tema "Non-Linear strain path (NLSP)"

A model is presented to calculate the rotation path of crystals under equibiaxial tension when the strain ratio is fixed (prescribed strain path) or when the strain ratio is allowed to adjust itself according to the external constraint and the current state of the plastic anisotropy of the material (nonprescribed strain path). It is found that the stability of grain orientation is related to the curvature of the strain path. There is a difference in the predicted equibiaxial deformation texture for the two types of strain paths. Grain orientations which are unstable under a linear strain path may become stable under a non-linear or varying strain path.

This paper adopts Macroscopic Phenomenological Method to establish constitutive relation. In order to maintain better approximation, it adopts testing data of typical stress path, testing data of uniaxial tension and torsion test. Applying multidimensional incremental theory under general loading law, on the base of certain loading function of stress space and loading function of strain space, this essay drives heat-elasto-plastic constitutive relation of heated isotropic hardening material under the condition of elasto-plastic decoupling. Meanwhile, this constitutive relation also suits for kinematic hardening material and elastic-perfectly plastic material. This paper builds a means of driving constitutive relation of multidimensional incremental theory under general loading law in strain space.

In this work, Forming Limit Curves (FLCs) of the conventional and pre-stretched High Strength Steel (HSS) sheet grade 440 (SCGA440-45) were investigated. The conventional forming limit curve was experimentally determined by using the Nakajima stretching test. Subsequently, the non-linear strain path FLCs were precisely developed through the Nakajima stretching test after the specimens were pre-stretched in biaxial direction up to several levels on the Marciniak In-plane stretching test. The gained non-linear strain path FLCs were compared with the conventional FLC.Additionally, the experimental Forming Limit Stress Curve (FLSCs) were calculated using the experimental FLC and non-linear strain path FLCs data from investigated steel sheet. The yield criterion Hill’48 was employed in combination with the Swift strain hardening law to describe anisotropic deformation and plastic flow behavior of the HSS sheet, respectively. Hereby, the influence of pre-stretching levels on the experimentally determined the FLCs and FLSCs were examined. The results prove a significant influence of the pre-stretching levels on the both FLCs and FLSCs of the investigated HSS sheet. For a low pre-stretching in biaxial loading the FLCs demonstrated a reduced formability and the FLSCs exhibited the limited stress levels depending on the experimental FLC data.

The application of modern materials plays an important role directly under the aspect of lightweight potential. To exploit these options effectively a numerical accurate reproduction of the material behavior is indispensable. Especially in the case of large deformations a directional and strain rate dependent hardening behavior can be observed. By disregarding this effect significant failure in the computed stress state can arise, which can conduct to a corruption of the spring-back forecast. Within this contribution a new test method for analyzing the evolution of subsequent yield loci under strain path changes for the aluminum alloy AA6016 and the deep drawing steel DC06 is presented. In the first stage of the experimental investigations, yield loci with linear strain paths were considered to characterize the material behavior for the initial condition. On further experiments with several stress states the strain path dependent hardening behavior of the material is determined. The non-linear strain paths are realized through uniaxial prestrained primary specimens with following extraction of secondary samples for following stress states, e.g. a modified ASTM simple shear test specimen. Subsequent yield loci are investigated and compared to the yield surfaces Hill48 and Barlat 2000 (Yld2000-2d) with an isotropic hardening behavior. With this study the evolution of the yield locus for prestrained specimens is evaluated. The research of the subsequent yield loci for strain path changes serves as basis for further scientific investigations with a view to assess different approaches of isotropic-kinematic hardening models in consideration of the analyzed steel and aluminum sheet metals.

In this paper, results of an experimental and numerical investigation of the effects of non-linear deformation on the fatigue crack growth in composite laminates are presented and discussed. Mode I fatigue fracture experiments are carried out on extended compact tension specimens under sinusoidal load control at a frequency of 4 Hz. The fatigue fracture test data are analysed using a power law relationship between the crack growth rates and the range of the path-independent J-integral. A two- dimensional finite element model of the extended compact tension specimen is set up in order to compute the J-integral values. The model is coupled with damage analysis in order to study the effect of non-linear deformation on the fatigue fracture performance. The damage analysis is based on the Tsai-Wu failure criterion. The non-linear model is verified by carrying out comparisons between the simulated mechanical behaviour of the extended compact tension specimen and the measured one. The damage distribution within the specimen is analyzed. The J-integral is computed over paths surrounding the crack tip and not crossing the damage zone. It is shown that taking into account the damage behaviour improves the fatigue fracture resistance, which is attributed to increased strain energy dissipation as a result of non-linear deformation.

Thermomechanical hot rolling processes are often realized using reverse rolling stands, where the rolled stock is fed forward and backward through the rolling gap. During those processes, material undergoes several strain reversals that significantly alter microstructure evolution of austenite with respect to continuously rolled counterparts. In Nb-microalloyed steels, where precipitation hardening is usually expected, the effects of strain reversal are especially complex. When rolling direction is reversed, both static recrystallization (SRX) kinetics and strain-induced precipitation (SIP) processes are slowed down due to decreasing dislocation density. It affects the competition between driving force for SRX and pinning pressure for SIP and, in turn, changes the non-recrystallization temperature (Tnr), compared to the case where strain path is linear. In the present paper, detailed through-scale analysis of strain path effects in microalloyed austenite will be presented. Physical simulation and detailed microstructural analysis will be employed to study global and local effects in microalloyed austenite after complex deformation histories. Conclusions regarding the influence of strain path changes on the interactions between SRX and SIP will be drawn.

Abstract Recent biaxial experiments on spruce wood show that consideration of an elliptic failure surface according to Tsai and Wu and an elastic model for stress states within this envelope lead to an insufficient description of the mechanical behavior. As compression perpendicular to the grain occurs, a non-linear stress path results from a proportional biaxial strain path. Investigation of characteristic samples with respect to loading-unloading-reloading cycles for states of stress below failure reveals behavior similar to what is known as hardening type plasticity. The experimentally observed mechanical behavior is described by means of a two-surface plasticity model addressing both failure and non-linear stress response below failure as separate mechanisms. Prediction of failure is achieved by means of a second-order failure envelope according to Tsai and Wu. The non-linear stress response has to be covered by a novel orthotropic hardening type plasticity model. Since available experimental data covers only plane stress in the LR-plane, both orthotropic failure and yield surfaces, respectively, are restricted to this case.

This paper presents the calculation of the cross‐section of an RC rod element strength under the quasistatic low‐cyclic loadings, considering the non‐linear stress‐strain relations of materials without cracks. Some mathematical models of the limit and shakedown analysis proposed by the authors involve the technique of calculating the cross‐section under one‐path loadings, considering the non‐uniqueness of problem solutions. The plasticity conditions for the materials of the cross‐section are formulated either in stress or in strain space. Simple solutions of two types, direct and inverse, corresponding to the limit states for alternating plasticity or progressive failure, are considered for the non‐linear optimization problems obtained. Santrauka Nagrinėjamas nepleišėjančio gelžbetoninio elemento skerspjūvio stiprio skaičiavimas veikiant mažaciklei apkrovai. Naudojama netiesinė medžiagos įtempių-deformacijų priklausomybė. Pateikiami ribinės pusiausvyros ir prisitaikomumo analizavimo uždavinių matematiniai modeliai. Naudojama metodika skerspjūvio parinkimui vienos trajektorijos apkrovimo atvejais, nagrinėjamas uždavinio sprendinių nevieninteliškumas. Medžiagos plastiškumo sąlygos formuluojamos įtempiais arba deformacijomis. Sprendžiant netiesinio optimizavimo uždavinius gaunami paprasti dviejų tipų sprendiniai: tiesioginis ir atvirkštinis, atitinkantys progresuojančio arba kintamo plastiškumo ribinius plastinio suirimo atvejus.

The effects of strain path reversal on the microstructure in AA5052 have been studied using high resolution EBSD. Deformation was carried out using two equal steps of forward/forward (F/F) or forward/reverse (F/R) torsion at a temperature of 300°C and strain rate of 1s-1 to a total strain of 0.5. In both cases the deformation microstructure in the majority of grains analysed consisted of microband arrays clustering at specific angles to the macroscopic deformation axes. For the F/F condition microbands clustered around -20° and +45° to the maximum principle stress direction, whilst for the F/R condition significantly more spread in microband angle was observed. This suggests that the microbands formed in the forward deformation have or are dissolving and any new microbands formed are related to the deformation conditions of the final strain path. This leads to the conclusion that instantaneous deformation mode determines the orientation of new microbands formed whilst a non-linear strain path history influences the range of misorientation angle in the material through the dissociation of previously formed microbands and the formation of new microbands at the new straining condition, leading to a lower level of misorientation angle. Analysis of material subjected to static annealing at 400°C for 1 hour appears to correspond with these observations as the F/F material was completely recrystallised with a fine grain structure whilst the F/R material had no major signs of recrystallisation.

Tube hydroforming process is a well-established manufacturing process widely employed to form tubular parts that are lighter and stronger compared to those from stampings. Nevertheless, determination of process loading paths, i.e. axial feed distance versus hydraulic pressure, still typically relies on trial-and-error FEM approach. In this paper, a semi-forward adaptive simulation concept is proposed as an effective FEM approach, able to select a feasible THF loading path within a single FEM simulation run. The semi-forward adaptive simulation technique is based on the ability to “adapt” or adjust the loading path as to keep the forming strains within a preferred stain trajectory over the course of a simulation run. Forming strains at the current simulation time step are used as inputs to the fuzzy logic control; the output sets are then used to readjust the loading path for the current and next time steps. This semi-forward adaptive simulation scheme allows one to “correct” the loading path at the current time step as well as to better predict the forming strains in the next time step. It was found that the corrective and predictive nature of this semi-forward simulation approach coupled with the strain trajectory based fuzzy logic control scheme could handle a highly non-linear forming behavior of tube hydroforming processes effectively. In this work, a feasible loading path was determined thru only one simulation run for successful hydroforming of an eccentric bulged tubular part.

This paper presents the weak formulation of a quasi-static evolution model for two deformable bodies with uni-directional adhesive unilateral contact on which external loads act. Small deformations and linearized elastoplasticity with hardening are assumed. The adhesion component is rate-dependent or rate-independent according to the choice of the viscosity coefficient of the glue; elastoplasticity is considered rate-independent. The weak formulation is expressed as a doubly non-linear problem with unbounded multivalued operators, as a function of internal and boundary displacements, plastic and symmetric strain tensors, and the bonding field and its gradient. This paper differs from other formulations by coupling the equations defined inside and on the boundary of the solids in functional form. In addition to this novelty, we verify the existence of solutions by a path other than that displayed in similar articles. The existence of solutions is demonstrated after considering a succession of doubly non-linear problems with an unbounded operator, and verifying that the solution of one of the problems is also a solution to the objective problem. The proof is supported by previous results from non-linear Partial differential equations theory with monotone operators.

Von Misses truss is one of the best examples to explain different theoretical approaches, nature of non-linear solution, define the snap-through, illustrate interactive buckling, etc. The presented paper compares two nonlinear approaches to the problem. Effect of nonlinear terms in strain-displacement relationship on the load level in critical point of nonlinear solution is analyzed. To obtain the nonlinear equilibrium paths, the Newton-Raphson iteration algorithm is used. Corresponding levels of the total potential energy are defined. The peculiarities of the effects of the initial imperfections are investigated. Custom FEM computer program has been used for analysis. Full Newton-Raphson procedure, in which the stiffness matrix is updated at every equilibrium iteration, has been applied. Obtained results are compared with results of the nonlinear analysis using ANSYS system, element type BEAM3 is used. The arc-length method is chosen for analysis, the reference arc-length radius is calculated from the load increment. Only fundamental path of nonlinear solution has been presented.

An improved mathematical model is presented to investigate the free vibration behavior of post-buckled tapered functionally graded material beam, subjected to uniform temperature rise and steady-state heat conduction. The material properties including the thermal conductivity are considered to be temperature-dependent and an iterative algorithm for solving temperature-dependent steady-state heat conduction equation is presented to get the correct temperature profile. The initial static post-buckling problem is formulated using minimum potential energy principle and the subsequent free vibration problem is formulated using Hamilton’s principle by employing the tangent stiffness of the post-buckled configuration. The solution of the governing equations is obtained using Ritz method. Following Timoshenko beam theory, a geometrically non-linear mathematical model is developed by employing the non-linear strain–displacement relationships for both normal and shear strains. The study is carried out for both hinged–hinged and clamped–clamped beams. Non-dimensional load–frequency behaviors are presented for different gradation indices, taperness parameters, and length–thickness ratios. Static post-buckling equilibrium path for clamped–clamped beams is also presented. The significant effects of shear non-linearity and temperature-dependent thermal conductivity on dynamics of tapered functionally graded material beam are shown in the paper.

In order to design efficient foundations, it is necessary to know exact behaviour of them and surrounding soil under the load. At present various numerical methods [1–11] are used to determine such response. The behaviour of axi-symmetric bored foundation is described in this paper. The finite element method is utilized in analysis of the foundation. Linear and non-linear properties of material are taken into account. The investigation of properties of soil, predominating in Lithuania, and economical constructing of foundation gives preference to bored foundation [12]. Schematically this type of foundation can be depicted as a cylindrical body resting on soil (Fig 1). Geometrically the foundation can be described through the diameter d and the height h. F denotes the vector of the axisymmetric load. Such bored foundation has ratio h/d ≥ 2 and transmit part of the external load through their side surface to soil. It is very difficult to achieve a shear failure of soil mass for such a type of foundation, but the foundation may suffer significant deflections. It is, therefore, important to known the stress-strain state of soil for design purpose. Various stress-strain models have been proposed for representing the behaviour of soil [14]. These range from very simple linear-elastic to complex elastic-plastic models. In general, the stress vector σ is related to the strain vector ε through the elasticity matrix [C] (1) [1,2]. The linear-elastic stress-strain model is the simplest. In this case matrix [C] is constant and history independent (2) [4]. More complex is the non-linear-elastic model. Two incremental linear-elastic approaches can be used to handle this problem [4]. In the first case a tangent and in the other—secant modulus are used. The described models imply that volume changes are induced by changes in mean normal effective stress alone, while shear strains are induced by shear stress alone. Investigation shows that volumetric strains are induced by changes in shear stress as well as by changes in the mean normal stress [4, 11]. This can be accounted for the dilatant-elastic stress-strain model. The incremental shear-induced volume change Δεv can be expressed in terms of a tangent dilation parameter αϵ [10] according to (4), in which Δγ is the increment of maximum shear strain [4]. The dilatant-elastic materials lead to a three parameter stress-strain model in which the increments of volumetric and shear strain are related to the corresponding stress increments according to (5). The most complex is the elastic-plastic stress-strain model. A basic assumption of elastic models is that the unloading path is identical to the loading path. This is generally not true for soils where the recoverable strain upon unloading is generally small. The recoverable strain is considered to be elastic, while the non-recoverable strain is considered to be plastic. There have been proposed various yield conditions to model those plastic properties of soils. Von Mises yield condition can be written (6) in terms of the second invariant of stress deviator J 2 and yield stress Y(κ) from uniaxial tests [2]. For soils, concrete and other ‘frictional’ materials the Drucker and Prager law (7) is frequently used [2,13]. In this law hydrostatic press σm is incorporated, while c and Φ are the cohesion and angle of friction, respectively [8]. The problem is formulated and analysed by the finite element method. The region of a model is subdivided into discrete elements. The global system of equations to be solved is described by the equation (9), where [K(U)] denotes the global non-linear stiffness matrix, U is the unknown deflection vector and F is the vector of nodal forces [1,2]. The matrix [K(U)] and the vector F can be made up by adding up the element stiffness matrices [k e(u e)] and the element nodal deflection vectors f e, respectively. Therefore the problem can be mathematically described through the governing equation of the separate element (10), where u e denotes the unknown element nodal deflection. The stiffness matrix can be determined from the principle of virtual work. This involves equating the work done by the internal stresses with that done by the nodal forces. In a non-linear analysis the matrix [k e(u e)] depends on the vector u e and solution of a problem must be obtained throughout the complete history of incremental load application [1]. Time is a convenient variable tthat denotes different intensities of load applications. Equality of virtual work is expressed through displacement increments Δu e in the time step Δt. In this case the relation of a governing equation is (11) where tpe , denotes nodal point forces corresponding to the element stresses at time t. A solution of (11) may be subject to very significant errors, it is, therefore, necessary to iterate until the solution is obtained to sufficient accuracy. The incremental equations, used in the Newton-Raphson iteration, are (12) and (13), for i= 1, 2, 3,…with the initial conditions shown in (14). The foundation and soil are considered a non-homogeneous deformable solid [2,4,9]. Two separate problems were formulated. The first problem deals with linear-elastic material properties. The other accounts for elastic-plastic properties of soil. Von Mises and Drucker-Prager yield conditions are applied. The formulation is geometrically linear and axisymmetric. The sketch of the model is depicted in Fig 2. The material properties of soil and concrete are chosen such, that predominate in Lithuania [15]. The ANSYS [5–8] computer code is used for the calculation. Another problem is to choose geometric dimensions of a soil model because it is possible to analyse the finite size model by finite element method. The width of a model D=3.75 d is chosen from the investigations of other authors [2, 9]. Some analyses were carried out in order to determine the influence of the soil depth under the foundation H = 2—4.333 h on the deflection at the top of the foundation. In this case the linear-elastic model was applied. The results are depicted in Fig 3. The depth H =2.167 h was chosen for further analysis. The generated discrete model was estimated for the quality. The model was under the circular in plane with the radius r = 0.4 m uniform distributed surface loading p = 1.989 MPa [16]. The calculated stress and strain distribution in soil under the centre of loading are compared, as shown in Fig 4 and 5, respectively. In case of non-linear analysis the load is applied in two stages. In the first stage the model is loaded by weight. The full external load p = 1.989 MPa is incrementally applied in the second stage. The history of load application is described through the time variable t. The history of the deflection at the top of the foundation is depicted in Fig 6. It seems that the deflection of linear model under the full 1 MN load and that of model, implemented with Drucker-Prager yield condition, differs by 11%. The distribution of accumulated equivalent plastic strain in the cross-section (Fig 7) of the model, utilizing the Drucker-Prager yield condition, shows that the biggest plastic deformation developed in the immediate contact with the foundation. The history of the principal stresses of the node under the foundation and Drucker-Prager and von Mises yield surfaces in principal stress space are depicted in Fig 8. Our analysis of axisymmetric bored foundation allows to know stress-strain state near the foundation. We can see that the external force of great magnitude cause significant plastic deformation, which, in turn, leads to significant deflection of the foundations.

The formation of fracture process zones in polygranular reactor core moderator graphites subjected to four-point bending has been investigated. The three-dimensional digital image correlation technique has been combined with resistance strain gauge measurements to evaluate, both the localised and the global displacements during testing. The non-linear load-displacement characteristics prior to peak load are correlated with the localised displacements which can extend up to ~3mm (process zone) from the tensile surface of the specimen. At peak load a macro-crack propagates rapidly along an irregular path controlled by the direction of the applied tensile load and the microstructure of the graphite. These cracks arrest prior to complete separation of the specimen. Localised tensile process zones extend for distances of up to ~3mm ahead of the tips of these cracks.

This work was aimed to experimentally and theoretically investigate the formability of a new magnesium alloy sheet at room temperature. The fracture forming limit diagram was predicted by MMC3 and DF2014 models, where the non-linear strain path effect was taken into account by means of damage accumulation law. In order to obtain the instantaneous values of the stress triaxiality and the Lode parameter during the deformation process, strains tracked by digital image correlation technique were transformed into stresses based on the constitutive equations. The fracture forming limit diagram predicted by the fracture models was compared with the forming limits obtained by ball punch deformation tests. The prediction errors were evaluated by the accumulative damage values, which verified the advantages of ductile fracture models in predicting the forming limits of the magnesium alloy sheets.

Springback occurs in sheet metal forming due to elastic strain recovery after removal of process forces respectively after opening of the tool. For this reason, a precise description of springback requires the elastic stress-strain relationship described by the Young’s modulus as well as the internal stress distribution of the part before unloading. In this context, the Bauschinger effect influences the stress state before springback due to premature plastification during load reversal or load path change. As is well known, the stress-strain curve of a material during unloading is non-linear because of additional microplastic strain, which is reflected in a decrease of the Young’s modulus. The aim of this work is to characterize the aforementioned phenomena and their effect on springback for three dual-phase steels namely DH800, DH1000 and DP1200LY. For this purpose, cyclic tensile-compression tests as well as loading and unloading loops within uniaxial tensile tests are performed at different plastic strains. To evaluate the springback behavior of the investigated materials, two different hat-profiles geometries are investigated. By comparing the springback of dual-phase steels on part level, the significance of different material influences with regard to springback is evaluated. The results show that the investigated dual-phase steels exhibit a pronounced Bauschinger effect and a considerable amount of microplastic strain with increasing total strain. However, the comparison between the springback of the hat-profiles and the determined material parameters proves a significant influence of the elastic strain on springback, while microplastic strain and the Bauschinger effect have a minor influence.

This paper presents a geometric non-linear finite element model of shape memory alloy composite plates and its source code in order to determine critical loads and to trace post-buckling paths of the composite plates. A numerical study was conducted on symmetric and anti-symmetric angle-ply and cross-ply composite plates. Buckling and post-buckling improvements of composite plates due to the shape memory effect behaviour of shape memory alloy were carried out. The pre-strained shape memory alloy wires were embedded within laminated composite plates so that recovery stress could be induced with the heated wires. The methods of active property tuning and active strain energy tuning were applied to show the various effects of the shape memory alloy on the studied behaviour. The result showed that significant improvements occurred in the critical loads and the post-buckling paths of the symmetric and anti-symmetric angle-ply and the symmetric cross-ply composite plates due to the active strain energy tuning method. In the case of the anti-symmetric cross-ply composite plate where bifurcation point did not exist, the post-buckling path was substantially improved.

Recent experimental studies revealed the presence of Volterra dislocation-type long-range elastic strain/stress field around a shear band (SB) terminated in a bulk metallic glass (BMG). The corollary from this finding is that shear bands can interact with these stress fields. In other words, the mutual behaviour of SBs should be affected by their stress fields superimposed with the external stresses. In order to verify this suggestion, the topography of the regions surrounding SBs terminated in the BMGs was carefully analysed. The surfaces of several BMGs, deformed by compression and indentation, were investigated with a high spatial resolution by means of scanning white-light interferometry (SWLI). Along with the evidence for the interaction between SBs, different scenarios of the SB propagation have been observed. Specifically, the SB path deviation, mutual blocking, and deflection of SBs were revealed along with the significant differences between the topologies of the mode II (in-plane) and mode III (out of plane) SBs. While the type II shear manifests a linear propagation path and a monotonically increasing shear offset, the type III shear is associated with a curved, segmented path and a non-monotonically varying shear offset. The systematic application of the “classic” elastic Volterra’s theory of dislocations to the behaviour of SBs in BMGs provides new insight into the widely reported experimental phenomena concerning the SB morphology, which is further detailed in the present work.

Increased urbanization causes traffic and parking issues especially in metropolitan cities like Karachi, London, Shanghai, etc. To accommodate parking issues for the vehicles mainly in urban areas (excavated) underground parking areas under or nearby high rise buildings are preferred. As a result of excavation, ground movements occur that have a major impact on structures, buildings, and utilities. The past research usually oversimplified surface structure as an equivalent elastic beam, which is unable to represent the behavior of a framed building realistically. In this study, the detrimental effects (i.e. crack pattern) on a two-floor RCC framed building founded on piles due to an adjacent excavation-induced ground movement are investigated. Elasto-plastic coupled-consolidation analysis was adopted. The hypoplastic constitutive model was used to capture soil behavior. It is an advanced model which is able to capture the soil unique features which are non-linear behavior, stiffness degradation (with stress, strain & path-dependent), and stress-strain dependent soil dilatancy. The concrete damaged plasticity (CDP) model was used to capture the cracking behavior in the concrete beams, columns and piles. It was revealed that the induced slope and tilting are not equal. Consequently, the frame was distorted. As a result, tension cracks were induced at the inner side of the column.

The grinding of riblets with multiple profiled grinding wheels is an efficient method to minimize the fluid friction on surfaces. In turbo machinery components, like pump impellers or compressor blades, the riblets must be ground with a curved tool path since the flow is rarely linear on such surfaces. This leads to angular errors in the generated riblet profiles and therefore requires the use of grinding wheels with smaller diameters. The tool wear increases due to lateral strain on the peaks of the grinding wheel. Consequently, the increased wear and the need of smaller tool diameters decrease the efficiency of the process. In this paper a structuring process with dicing blades was investigated in order to increase the economic viability of this process. A dressing operation for such tools is not necessary and thus reduces the non-productive time of the manufacturing process. Furthermore, profile tip wear has no negative effects on the aspect ratio of the generated riblets since the riblet geometry is determined by the thickness of the dicing blades.

The main goal of this study was to investigate the effect of tow tension and related internal micro-structure on the damage behavior of 3D orthogonal woven composites under tensile loading. For representing the internal micro-structure of the composite with respect to varying tow cross-section and the unregulated undulated path which are introduced by Z-binder tension, a dynamical method at filament level which simulates an interlacing process was used to obtain the fabric architecture. Then, an element recognition algorithm was proposed to convert a representative unit cell of 3D woven fabric architectures into a finite element model with 8-node solid elements consisting of four kinds of sets in terms of warp, weft, Z-binder tows and resin matrix. In addition, filament trajectory was also extracted from fabric architecture to serve as a local material orientation. Comparative simulations under tensile loading were conducted on the FEA models generated by this work and texgen software, respectively. An experiment was also carried out to verify the simulation results. The stress–strain curve in the proposed model was found to be closer to the experiment data. The results show that the tensile modulus and strength reduce due to the diverged warp tow path which is induced by the interaction between the tows during the weaving process. Moreover, the irregularity and compressed weft tow cross-sections nearby the intercross point are more likely to generate the transverse damage which would result in the non-linear tensile behavior of the composite material.

In order to represent the mechanical response laws of high-modulus asphalt pavement (HMAP) faithfully and objectively, the viscoelasticity of high-modulus asphalt mixture (HMAM) was considered, and the viscoelastic mechanical responses were calculated systematically based on moving load by numerical simulations. The performances of the HMAP in resistance to the deformation and the cracking at the bottom layer were compared with the ordinary asphalt pavement. Firstly, Lubao and Honeywell 7686 (H7686) were selected as the high modulus modifiers. The laboratory investigations of Asphalt mix-70 penetration, Asphalt mix-SBS (styrene-butadiene-styrene), HMAM-Lubao and HMAM-H7686 were carried out by dynamic modulus tests and wheel tracking tests. The conventional performances related to the purpose of using the HMAM were indicated. The master curves of the storage moduli were obtained and the viscoelastic parameters were fitted based on viscoelastic theories. Secondly, 3D pavement models based on moving loads for the viscoelastic structures were built using the non-linear finite element software ABAQUS. The wheel path was discretized in time and space to apply the Haversine wave load, and then the mechanical responses of four kinds of asphalt pavement were calculated. Finally, the sensitivity analysis was carried out. The results showed that the addition of the high modulus modifiers can improve the resistance to high-temperature rutting of the pavements. Except for the tensile strain and stress at the bottom of the underlayer, other responses decreased with the increases of the dynamic moduli and the change laws of the tensile strain and stress were affected by the range of the dynamic modulus. The tensile stress at the bottom of the asphalt layer would be too large if the modulus of the layer were too large, and a larger tensile strain would result. Therefore, the range of the modulus must be restricted to avoid the cracking due to excessive tension when using the HMAM. The resistance of the HMAP to deformation was better and the HMAP was less sensitive to load changes and could better withstand the adverse effects inflicted by heavy loads.

The stress-strain response of the basic concrete making material, i.e. the mortar and aggregates, are well known. In general, the aggregate behaves linearly up till failure, possessing a very high ultimate compression strength and stiffness. The behavior of mortar is non-linear, even at low loading levels. The resulting composite material, the concrete, exhibits a less stiff response, in combination with degradation in strength. This study looked into the influence of the inclusion-to-specimen volume ratio of a 100x100x50 mm mortar specimen. Two inclusion configurations were considered, parallel and diagonal to the line of loading, while the ratio varied from zero to 0.66. It was shown that the inclusion-to-specimen volume ratio strongly influenced the strength, the stiffness, and failure mode. The strength behavior had a minimum and a maximum bifurcation point, while the stiffness response increased, as a function of an increase in the inclusion-to-specimen volume ratio. Visual observation of the cracking pattern revealed that the initial cracking was always situated at the interface between the aggregate and mortar in tension and propagated through the mortar matrix. It was also perceived that the crack propagation path of the very dense, diagonally arranged inclusions deviated from the columnar configuration observed from the parallel inclusion formation. These densely diagonally arranged aggregates also resulted in spalling in the lateral direction.

This paper presents a summary of the life prediction methods developed under the NASA Lewis Research Center’s Hot Section Technology (HOST) program. A major objective of the fatigue and fracture efforts under the HOST program was to significantly improve the analytic life prediction tools used by the aeronautical gas turbine engine industry. This has been achieved in the areas of high-temperature thermal and mechanical fatigue of bare and coated high-temperature superalloys. Such technical improvements will eventually reduce life cycle costs. The cyclic crack initiation and propagation resistance of nominally isotropic polycrystalline alloys and highly anisotropic single crystal alloys have been addressed. A sizeable data base has been generated for three alloys [cast PWA 1455 (B–1900 + Hf), wrought Inconel 718, and cast single-crystal PWA 1480] in bare and coated conditions. Two coating systems, diffusion aluminide (PWA 273) and plasma-sprayed MCrAlY overlay (PWA 286), were employed. Life prediction modeling efforts were devoted to creep-fatigue interaction, oxidation, coatings interactions, multiaxially of stress-strain states, mean stress effects, cumulative damage, and thermomechanical fatigue. The fatigue crack initiation life models developed to date include the Cyclic Damage Accumulation (CDA) Model of Pratt & Whitney and the Total Strain Version of Strainrange Partitioning (TS-SRP) of NASA Lewis for nominally isotropic materials, and the Tensile Hysteretic Energy Model of Pratt & Whitney for anisotropic superalloys. The fatigue model being developed by the General Electric Company is based upon the concepts of Path-Independent Integrals (PII) for describing cyclic crack growth under complex non-linear response at the crack tip due to thermomechanical loading conditions. A micromechanistic oxidation crack extension model has been derived by researchers at Syracuse University. The models are described and discussed in the paper. Only limited verification has been achieved to date as several of the technical programs are still in progress and the verification tasks are scheduled, quite naturally, near the conclusion of the program. To date, efforts have concentrated on developement of independent models for cyclic constitutive behavior, cyclic crack initiation, and cyclic crack propagation. The transition between crack initiation and crack propagation has not been thoroughly researched as yet, and the integration of these models into a unified life prediction method has not been addressed.

AbstractWe present the fabrication and electromechanical characterization of a class of polymeric high-elongation strain sensors. Samples of polydimethylsiloxane were coated with Creative Materials, Inc.'s 123-27 Electrically Conductive Silicone Ink and the resistance behavior was evaluated in uniaxial tensile tests. Large strains (up to 100%) were observed with monotonically increasing resistance changes. A clear, linear trend up to 65% strain dominated the resistance vs. strain behavior then resistance increased non-linearly. Image processing of the film coupled with a finite element conduction simulation indicate the change in resistance is primarily a geometric effect. Both the conduction path and the polydimethylsiloxane substrate break completely around 100% strain. The samples exhibit a gauge factor of approximately 10.

AbstractWe propose and implement a computational procedure to establish data-driven surrogate constitutive models for heterogeneous materials. We study the multiaxial response of non-linear n-phase composites via Finite Element (FE) simulations and computational homogenisation. Pseudo-random, multiaxial, non-proportional histories of macroscopic strain are imposed on volume elements of n-phase composites, subject to periodic boundary conditions, and the corresponding histories of macroscopic stresses and plastically dissipated energy are recorded. The recorded data is used to train surrogate, phenomenological constitutive models based on neural networks (NNs), and the accuracy of these models is assessed and discussed. We analyse heterogeneous composites with hyperelastic, viscoelastic or elastic–plastic local constitutive descriptions. In each of these three cases, we propose and assess optimal choices of inputs and outputs for the surrogate models and strategies for their training. We find that the proposed computational procedure can capture accurately and effectively the response of non-linear n-phase composites subject to arbitrary mechanical loading.

RESUMO: Neste trabalho descreve-se analiticamente de maneira detalhada a detecção e a classificação de pontos críticos na trajetória primária de equilíbrio de sistemas estruturais. Utiliza-se a Formulação Lagrangiana Total para descrever a cinemática de um elemento de barra biarticulado 2D. Através desta formulação obtém-se o vetor de forças internas e a matriz de rigidez tangente que levam em conta os efeitos da não linearidade geométrica. Assume-se um modelo constitutivo linear elástico para o estado uniaxial de tensão-deformação, usando a deformação de Green-Lagrange e a tensão axial do segundo tensor de Piola-Kirchhoff que são energeticamente conjugados. Como estudo de caso apresenta-se uma treliça plana hiperestática composta com 3 elementos biarticulados 2D e com dois graus de liberdade. Por fim, determinam-se as condições geométricas e físicas para a coalescência entre os pontos limites e de bifurcação. A principal contribuição deste trabalho é demonstrar a necessidade de compreender melhor os fenômenos não lineares para projetar sistemas estruturais mais seguros. ABSTRACT: Using an analytical this paper describes in detail the detection and classification of critical points in the primary equilibrium path of structural systems. The Total Lagrangian formulation is employed to describe the kinematics of a 2D bar element. With this formulation, the internal force vector and the tangent stiffness matrix including the geometric nonlinearity effects are obtained. An elastic linear constitutive model is assumed for the uniaxial stress-strain state. Such model uses the Green-Lagrange strain tensor and the second Piola-Kirchhoff axial stress tensor which are energetically conjugate tensors. As a study case, the article presents a statically inderminate plane truss discretized with three 2D bar elements. Finally, the geometrical and physical conditions for the coalescence between limit and bifurcation points are determined. The main contribution of this work is to demonstrate the need to better understanding the non linear phenomena. Such understanding is necessary for designing safer structural systems.

AbstractWe report on an investigation into the interfacial structure of undoped GaInAs/GaInAsP multiple quantum wells grown by metalorganic chemical vapour deposition (MOCVD), which exhibit a pronounced blue shift in luminescence output upon in-situ thermal annealing at 750°C. Using a recently developed composition mapping technique based on the scanning transmission electron microscope (STEM) in conjunction with energy dispersive X-ray (EDX) analysis, the constituent element concentration profiles across the interdiffused multilayer interfaces are measured with a spatial resolution of less than 2nm and a precision of better than 2–3%. The accuracy of the analysis is significantly improved by employing stoichiometric normalisation factors which compensate for systematic errors due to electron channelling. The results showed that the interdiffusion follows a highly non-linear path due to the relatively fast diffusion of the group V species compared to that of the group III species. This implies an increase in the coherency strain in the multilayer, a result which is supported by five-crystal Xray diffraction analysis of the layers. The samples have also been examined by high resolution electron microscopy (HREM) under chemically sensitive imaging conditions. The analysis of the interfacial chemical profile using HREM must be performed under analysis conditions for which a known and unique relationship between image contrast and composition occurs. This condition may not be satisfied in cases in which more than two chemical constituents interdiffuse and the diffusivities of these elements are not equal, as a range of similar lattice fringe motifs across the interface, representing different “diffusion paths”, could occur. The complementary nature of information provided by HREM and STEM provides a means of resolving this ambiguity.

This paper will compare the metaphoric structuring of the ecological concept of resilience—with its roots in Holling's 1973 paper; with psychological concepts of resilience which followed from research—such as Werner, Bierman, and French and Garmezy and Streitman) published in the early 1970s. This metaphoric analysis will expose the difference between complex adaptive systems models of resilience in ecology and studies related to resilience in relation to climate change; compared with the individualism of linear equilibrium models of resilience which have dominated discussions of resilience in psychology and economics. By examining the ontological commitments of these competing metaphors, I will show that the individualistic concept of resilience which dominates psychological discussions of resilience is incompatible with the ontological commitments of ecological concepts of resilience. Because the ontological commitments of the concepts of ecological resilience on the one hand, and psychological resilience on the other, are so at odds with one another, it is important to be clear which concept of resilience is being evaluated for its adequacy as a concept. Having clearly distinguished these competing metaphors and their ontological commitments, this paper will show that it is the complex adaptive systems model of resilience from ecology, not the individualist concept of psychological resilience, that has been utilised by both the academic discussions of adaptation to climate change, and the operationalisation of the concept of resilience by social movements like the permaculture, ecovillage, and Transition Towns movements. Ontological Metaphors My analysis of ontological metaphors draws on insights from Kuhn's (114) account of gestalt perception in scientific paradigm shifts; the centrality of the role of concrete analogies in scientific reasoning (Masterman 77); and the theorisation of ontological metaphors in cognitive linguistics (Gärdenfors). Figure 1: Object Ontological commitments reflect the shared beliefs within a community about the sorts of things that exist. Our beliefs about what exists are shaped by our sensory and motor interactions with objects in the physical world. Physical objects have boundaries and surfaces that separate the object from not-the-object. Objects have insides and outsides, and can be described in terms of more-or-less fixed and stable “objective” properties. A prototypical example of an “object” is a “container”, like the example shown in Figure 1. Ontological metaphors allow us to conceive of “things” which are not objects as if they were objects by picking “out parts of our experience and treat them as [if they were] discrete entities or substances of a uniform kind” (Lakoff and Johnson 25). We use ontological metaphors when we imagine a boundary around a collection of things, such as the members of a team or trees in a forest, and conceive of them as being in a container (Langacker 191–97). We can then think of “things” like a team or forest as if they were a single entity. We can also understand processes and activities as if they were things with boundaries. Whether or not we characterise some aspect of our experience as a noun (a bounded entity) or as a verb (a process that occurs over time) is not determined by the nature of things in themselves, but by our understanding and interpretation of our experience (Langacker 233). In this paper I employ a technique that involves examining the details of “concrete images” from the source domains for metaphors employed in the social sciences to expose for analysis their ontological commitments (Harrison, “Politics” 215; Harrison, “Economics” 7). By examining the ontological metaphors that structure the resilience literature I will show how different conceptions of resilience reflect different beliefs and commitments about the sorts of “things” there are in the world, and hence how we can study and understand these “things.” Engineering Metaphors In his discussion of engineering resilience, Holling (“Engineering Vs. Ecological” 33) argues that this conception is the “foundation for economic theory”, and defined in terms of “resistance to disturbance and the speed of return to the equilibrium” or steady state of the system. Whereas Holling takes his original example of the use of the engineering concept of resilience from economics, Pendall, Foster, & Cowell (72), and Martin-Breen and Anderies (6) identify it as the concept of resilience that dominates the field of psychology. They take the stress loading of bridges to be the engineering source for the metaphor. Figure 2: Pogo stick animation (Source: Blacklemon 67, CC http://en.wikipedia.org/wiki/File:Pogoanim.gif). In order to understand this metaphor, we need to examine the characteristics of the source domain for the metaphor. A bridge can be “under tension, compression or both forces at the same time [and] experiences what engineers define as stress” (Matthews 3). In order to resist these forces, bridges need to be constructed of material which “behave much like a spring” that “strains elastically (deforms temporarily and returns to its original shape after a load has been removed) under a given stress” (Gordon 52; cited in Matthews). The pogostick shown in Figure 2 illustrates how a spring returns to its original size and configuration once the load or stress is removed. WGBH Educational Foundation provides links to simple diagrams that illustrate the different stresses the three main designs of bridges are subject to, and if you compare Computers & Engineering's with Gibbs and Bourne's harmonic spring animation you can see how both a bridge under live load and the pogostick in Figure 2 oscillate just like an harmonic spring. Subject to the elastic limits of the material, the deformation of a spring is proportional to the stress or load applied. According to the “modern theory of elasticity [...] it [is] possible to deduce the relation between strain and stress for complex objects in terms of intrinsic properties of the materials it is made of” (“Hooke’s Law”). When psychological resilience is characterised in terms of “properties of individuals [that] are identified in isolation” (Martin-Breen and Anderies 12); and in terms of “behaviours and attributes [of individuals] that allow people to get along with one another and to succeed socially” (Pendall, Foster, and Cowell 72), they are reflecting this engineering focus on the properties of materials. Martin-Breen and Anderies (42) argue that “the Engineering Resilience framework” has been informed by ontological metaphors which treat “an ecosystem, person, city, government, bridge, [or] society” as if it were an object—“a unified whole”. Because this concept of resilience treats individuals as “objects,” it leads researchers to look for the properties or characteristics of the “materials” which individuals are “made of”, which are either elastic and allow them to “bounce” or “spring” back after stress; or are fragile and brittle and break under load. Similarly, the Designers Institute (DINZ), in its conference on “Our brittle society,” shows it is following the engineering resilience approach when it conceives of a city or society as an object which is made of materials which are either “strong and flexible” or “brittle and fragile”. While Holling characterises economic theory in terms of this engineering metaphor, it is in fact chemistry and the kinetic theory of gases that provides the source domain for the ontological metaphor which structures both static and dynamic equilibrium models within neo-classical economics (Smith and Foley; Mirowski). However, while springs are usually made out of metals, they can be made out of any “material [that] has the required combination of rigidity and elasticity,” such as plastic, and even wood (in a bow) (“Spring (device)”). Gas under pressure turns out to behave the same as other springs or elastic materials do under load. Because both the economic metaphor based on equilibrium theory of gases and the engineering analysis of bridges under load can both be subsumed under spring theory, we can treat both the economic (gas) metaphor and the engineering (bridge) metaphor as minor variations of a single overarching (spring) metaphor. Complex Systems Metaphors Holling (“Resilience & Stability” 13–15) critiques equilibrium models, arguing that non-deterministic, complex, non-equilibrium and multi-equilibrium ecological systems do not satisfy the conditions for application of equilibrium models. Holling argues that unlike the single equilibrium modelled by engineering resilience, complex adaptive systems (CAS) may have multi or no equilibrium states, and be non-linear and non-deterministic. Walker and Salt follow Holling by calling for recognition of the “dynamic complexity of the real world” (8), and that “these [real world] systems are complex adaptive systems” (11). Martin-Breen and Anderies (7) identify the key difference between “systems” and “complex adaptive systems” resilience as adaptive capacity, which like Walker and Salt (xiii), they define as the capacity to maintain function, even if system structures change or fail. The “engineering” concept of resilience focuses on the (elastic) properties of materials and uses language associated with elastic springs. This “spring” metaphor emphasises the property of individual components. In contrast, ecological concepts of resilience examine interactions between elements, and the state of the system in a multi-dimensional phase space. This systems approach shows that the complex behaviour of a system depends at least as much on the relationships between elements. These relationships can lead to “emergent” properties which cannot be reduced to the properties of the parts of the system. To explain these relationships and connections, ecologists and climate scientists use language and images associated with landscapes such as 2-D cross-sections and 3-D topology (Holling, “Resilience & Stability” 20; Pendall, Foster, and Cowell 74). Figure 3 is based on an image used by Walker, Holling, Carpenter and Kinzig (fig. 1b) to represent possible states of ecological systems. The “basins” in the image rely on our understanding of gravitational forces operating in a 3-D space to model “equilibrium” states in which the system, like the “ball” in the “basin”, will tend to settle. Figure 3: (based on Langston; in Walker et al. fig. 1b) – Tipping Point Bifurcation Wasdell (“Feedback” fig. 4) adapted this image to represent possible climate states and explain the concept of “tipping points” in complex systems. I have added the red balls (a, b, and c to replace the one black ball (b) in the original which represented the state of the system), the red lines which indicate the path of the ball/system, and the black x-y axis, in order to discuss the image. Wasdell (“Feedback Dynamics” slide 22) takes the left basin to represents “the variable, near-equilibrium, but contained dynamics of the [current] glacial/interglacial period”. As a result of rising GHG levels, the climate system absorbs more energy (mostly as heat). This energy can force the system into a different, hotter, state, less amenable to life as we know it. This is shown in Figure 3 by the system (represented as the red ball a) rising up the left basin (point b). From the perspective of the gravitational representation in Figure 3, the extra energy in the basin operates like the rotation in a Gravitron amusement ride, where centrifugal force pushes riders up the sides of the ride. If there is enough energy added to the climate system it could rise up and jump over the ridge/tipping point separating the current climate state into the “hot earth” basin shown on the right. Once the system falls into the right basin, it may be stuck near point c, and due to reinforcing feedbacks have difficulty escaping this new “equilibrium” state. Figure 4 represents a 2-D cross-section of the 3-D landscape shown in Figure 3. This cross-section shows how rising temperature and greenhouse gas (GHG) concentrations in a multi-equilibrium climate topology can lead to the climate crossing a tipping point and shifting from state a to state c. Figure 4: Topographic cross-section of possible climate states (derived from Wasdell, “Feedback” 26 CC). As Holling (“Resilience & Stability”) warns, a less “desirable” state, such as population collapse or extinction, may be more “resilient”, in the engineering sense, than a more desirable state. Wasdell (“Feedback Dynamics” slide 22) warns that the climate forcing as a result of human induced GHG emissions is in fact pushing the system “far away from equilibrium, passed the tipping point, and into the hot-earth scenario”. In previous episodes of extreme radiative forcing in the past, this “disturbance has then been amplified by powerful feedback dynamics not active in the near-equilibrium state [… and] have typically resulted in the loss of about 90% of life on earth.” An essential element of system dynamics is the existence of (delayed) reinforcing and balancing causal feedback loops, such as the ones illustrated in Figure 5. Figure 5: Pre/Predator model (Bellinger CC-BY-SA) In the case of Figure 5, the feedback loops illustrate the relationship between rabbit population increasing, then foxes feeding on the rabbits, keeping the rabbit population within the carrying capacity of the ecosystem. Fox predation prevents rabbit over-population and consequent starvation of rabbits. The reciprocal interaction of the elements of a system leads to unpredictable nonlinearity in “even seemingly simple systems” (“System Dynamics”). The climate system is subject to both positive and negative feedback loops. If the area of ice cover increases, more heat is reflected back into space, creating a positive feedback loop, reinforcing cooling. Whereas, as the arctic ice melts, as it is doing at present (Barber), heat previously reflected back into space is absorbed by now exposed water, increasing the rate of warming. Where negative feedback (system damping) dominates, the cup-shaped equilibrium is stable and system behaviour returns to base when subject to disturbance. [...]The impact of extreme events, however, indicates limits to the stable equilibrium. At one point cooling feedback loops overwhelmed the homeostasis, precipitating the "snowball earth" effect. […] Massive release of CO2 as a result of major volcanic activity […] set off positive feedback loops, precipitating runaway global warming and eliminating most life forms at the end of the Permian period. (Wasdell, “Topological”) Martin-Breen and Anderies (53–54), following Walker and Salt, identify four key factors for systems (ecological) resilience in nonlinear, non-deterministic (complex adaptive) systems: regulatory (balancing) feedback mechanisms, where increase in one element is kept in check by another element; modularity, where failure in one part of the system will not cascade into total systems failure; functional redundancy, where more than one element performs every essential function; and, self-organising capacity, rather than central control ensures the system continues without the need for “leadership”. Transition Towns as a Resilience Movement The Transition Town (TT) movement draws on systems modelling of both climate change and of Limits to Growth (Meadows et al.). TT takes seriously Limits to Growth modelling that showed that without constraints in population and consumption the world faces systems collapse by the middle of this century. It recommends community action to build as much capacity as possible to “maintain existence of function”—Holling's (“Engineering vs. Ecological” 33) definition of ecological resilience—in the face of failing economic, political and environmental systems. The Transition Network provides a template for communities to follow to “rebuild resilience and reduce CO2 emissions”. Rob Hopkins, the movements founder, explicitly identifies ecological resilience as its central concept (Transition Handbook 6). The idea for the movement grew out of a project by (2nd year students) completed for Hopkins at the Kinsale Further Education College. According to Hopkins (“Kinsale”), this project was inspired by Holmgren’s Permaculture principles and Heinberg's book on adapting to life after peak oil. Permaculture (permanent agriculture) is a design system for creating agricultural systems modelled on the diversity, stability, and resilience of natural ecosystems (Mollison ix; Holmgren xix). Permaculture draws its scientific foundations from systems ecology (Holmgren xxv). Following CAS theory, Mollison (33) defines stability as “self-regulation”, rather than “climax” or a single equilibrium state, and recommends “diversity of beneficial functional connections” (32) rather than diversity of isolated elements. Permaculture understands resilience in the ecological, rather than the engineering sense. The Transition Handbook (17) “explores the issues of peak oil and climate change, and how when looked at together, we need to be focusing on the rebuilding of resilience as well as cutting carbon emissions. It argues that the focus of our lives will become increasingly local and small scale as we come to terms with the real implications of the energy crisis we are heading into.” The Transition Towns movement incorporate each of the four systems resilience factors, listed at the end of the previous section, into its template for building resilient communities (Hopkins, Transition Handbook 55–6). Many of its recommendations build “modularity” and “self-organising”, such as encouraging communities to build “local food systems, [and] local investment models”. Hopkins argues that in a “more localised system” feedback loops are tighter, and the “results of our actions are more obvious”. TT training exercises include awareness raising for sensitivity to networks of (actual or potential) ecological, social and economic relationships (Hopkins, Transition Handbook 60–1). TT promotes diversity of local production and economic activities in order to increase “diversity of functions” and “diversity of responses to challenges.” Heinberg (8) wrote the forward to the 2008 edition of the Transition Handbook, after speaking at a TotnesTransition Town meeting. Heinberg is now a senior fellow at the Post Carbon Institute (PCI), which was established in 2003 to “provide […] the resources needed to understand and respond to the interrelated economic, energy, environmental, and equity crises that define the 21st century [… in] a world of resilient communities and re-localized economies that thrive within ecological bounds” (PCI, “About”), of the sort envisioned by the Limits to Growth model discussed in the previous section. Given the overlapping goals of PCI and Transition Towns, it is not surprising that Rob Hopkins is now a Fellow of PCI and regular contributor to Resilience, and there are close ties between the two organisations. Resilience, which until 2012 was published as the Energy Bulletin, is run by the Post Carbon Institute (PCI). Like Transition Towns, Resilience aims to build “community resilience in a world of multiple emerging challenges: the decline of cheap energy, the depletion of critical resources like water, complex environmental crises like climate change and biodiversity loss, and the social and economic issues which are linked to these. […] It has [its] roots in systems theory” (PCI, “About Resilience”). Resilience.org says it follows the interpretation of Resilience Alliance (RA) Program Director Brian Walker and science writer David Salt's (xiii) ecological definition of resilience as “the capacity of a system to absorb disturbance and still retain its basic function and structure.“ Conclusion This paper has analysed the ontological metaphors structuring competing conceptions of resilience. The engineering resilience metaphor dominates in psychological resilience research, but is not adequate for understanding resilience in complex adaptive systems. Ecological resilience, on the other hand, dominates in environmental and climate change research, and is the model of resilience that has been incorporated into the global permaculture and Transition Towns movements. References 2nd year students. Kinsale 2021: An Energy Descent Action Plan. Kinsale, Cork, Ireland: Kinsale Further Education College, 2005. 16 Aug. 2013 ‹http://transitionculture.org/wp-content/uploads/KinsaleEnergyDescentActionPlan.pdf>. Barber, Elizabeth. “Arctic Ice Continues to Thin, and Thin, European Satellite Reveals.” Christian Science Monitor 11 Sep. 2013. 25 Sep. 2013 ‹http://www.csmonitor.com/Environment/2013/0911/Arctic-ice-continues-to-thin-and-thin-European-satellite-reveals>. Bellinger, Gene. “Prey/Predator Model.” SystemsWiki 23 Nov. 2009. 16 Aug. 2013 ‹http://systemswiki.org/index.php?title=Prey/Predator_Model>. Blacklemon67. "Pogo Animation." Wikipedia 2007. 24 Sep. 2013 ‹http://en.wikipedia.org/wiki/File:Pogoanim.gif>. Computers & Engineering. Bridge Trucks Animated Stress Plot 1. 2003. GIF file. SAP2000 Bridge Design. ‹http://www.comp-engineering.com/announce/bridge/demo/truck_1.gif>. DINZ. “Resilience Engineering: 'Our Brittle Society' - The Sustainability Society - May 18th 2012.” The Designers Institute. 2013. 11 Aug. 2013 ‹http://www.dinz.org.nz/Events/2012/May/47965>. Gärdenfors, Peter. “Cognitive Semantics and Image Schemas with Embodied Forces.” Embodiment in Cognition and Culture. Ed. John Michael Krois et al. John Benjamins Publishing, 2007. 57–76. 8 Nov. 2012 ‹http://oddelki.ff.uni-mb.si/filozofija/files/Festschrift/Dunjas_festschrift/gardenfors.pdf>. Garmezy, N, and S Streitman. “Children at Risk: The Search for the Antecedents of Schizophrenia. Part I. Conceptual Models and Research Methods.” Schizophrenia Bulletin 8 (1974): 14–90. NCBI PubMed 14 Aug. 2013 ‹http://schizophreniabulletin.oxfordjournals.org/content/1/8/14.full.pdf>. Gibbs, Keith, and John Bourne. “The Helical Spring.” Schoolphysics 2013. 15 Aug. 2013 ‹http://www.schoolphysics.co.uk/animations/Helical_spring_shm/index.html>. Gordon, James Edward. Structures: Or, Why Things Don’t Fall Down. London: Plenum Press, 1978. Harrison, Karey. “Image Schemas and Political Ontology.” Communication, Cognition and Media: Political and Economic Discourse. Ed. Augusto Soares da Silva et al. Portugal: Aletheia, forthcoming. ———. “Ontological Commitments of Ethics and Economics.” Economic Thought 2.1 (2013): 1–19. 23 Apr. 2013 ‹http://et.worldeconomicsassociation.org/article/view/64>. Heinberg, Richard. Powerdown: Options and Actions for a Post-carbon World. New Society Publishers, 2004. Holling, Crawford Stanley. “Engineering Resilience versus Ecological Resilience.” Engineering within Ecological Constraints. Ed. Peter Schulze. Washington, DC: National Academy Press, 1996. 31–44. 11 Aug. 2013 ‹http://www.nap.edu/openbook.php?record_id=4919&page=31>. ———. “Resilience and Stability of Ecological Systems.” Annual Review of Ecology and Systematics 4.1 (1973): 1–23. 11 Aug. 2013 ‹http://webarchive.iiasa.ac.at/Admin/PUB/Documents/RP-73-003.pdf>. Holmgren, David. Permaculture: Principles & Pathways beyond Sustainability. Holmgren Design Services, 2002. Hopkins, Rob. “Kinsale Energy Descent Action Plan (2005).” Transition Culture: an Evolving Exploration into the Head, Heart and Hands of Energy Descent. n.d. 16 Aug. 2013 ‹http://transitionculture.org/essential-info/pdf-downloads/kinsale-energy-descent-action-plan-2005/>. ———. The Transition Handbook: From Oil Dependency to Local Resilience. Green Books, 2008. Print. ———. The Transition Handbook: From Oil Dependency to Local Resilience. Free edit version. ‹http://www.appropedia.org/Category:The_Transition_Handbook: Appropedia.org> 2010. 16 Aug. 2010 ‹http://www.cs.toronto.edu/~sme/CSC2600/transition-handbook.pdf>. Kuhn, Thomas. The Structure of Scientific Revolutions. 2nd ed. University of Chicago Press, 1962. Lakoff, George, and Mark Johnson. Metaphors We Live By. University of Chicago Press, 1980. Langacker, Ronald W. Foundations of Cognitive Grammar: Theoretical Prerequisites. Vol. 1. Stanford University Press, 1987. Langston, Art. “Tipping Point” or Bifurcation Between Two Attractor Basins. 2004. 25 Sep. 2013. ‹http://www.ecologyandsociety.org/vol9/iss2/art5/figure1.html>. Martin-Breen, Patrick, and J. Marty Anderies. Resilience: A Literature Review. Rockefeller Foundation, 2011. 8 Aug. 2013 ‹http://www.rockefellerfoundation.org/blog/resilience-literature-review>. Masterman, Margaret. “The Nature of a Paradigm.” Criticism and the Growth of Knowledge. Eds. Imre Lakatos & Alan Musgrave. Cambridge University Press, 1970. 59–89. Matthews, Theresa. “The Physics of Bridges.” Yale-New Haven Teachers Institute. 2013. 14 Aug. 2013 ‹http://www.yale.edu/ynhti/curriculum/units/2001/5/01.05.08.x.html>. Meadows, Donella H. et al. The Limits to Growth: A Report for the Club of Rome’s Project on the Predicament of Mankind. Universe Books, 1972. Mirowski, Philip. “From Mandelbrot to Chaos in Economic Theory.” Southern Economic Journal 57.2 (1990): 289–307. Mollison, Bill. Permaculture: A Designers’ Manual. Tagari Publications, 1988. PCI. “About.” Post Carbon Institute. 16 July 2012. 16 Aug. 2013 ‹http://www.postcarbon.org/about/>. ———. “About Resilience.org.” Resilience 16 July 2012. 16 Aug. 2013 ‹http://www.resilience.org/about>. Pendall, Rolf, Kathryn A. Foster, and Margaret Cowell. “Resilience and Regions: Building Understanding of the Metaphor.” Cambridge Journal of Regions, Economy and Society 3.1 (2010): 71–84. 4 Aug. 2013 ‹http://cjres.oxfordjournals.org/content/3/1/71>. RA. “About RA.” Resilience Alliance 2013. 16 Aug. 2013 ‹http://www.resalliance.org/index.php/about_ra>. Smith, Eric, and Duncan K. Foley. “Classical Thermodynamics and Economic General Equilibrium Theory.” Journal of Economic Dynamics and Control 32.1 (2008): 7–65. Transition Network. “About Transition Network.” Transition Network. 2012. 16 Aug. 2013 ‹http://www.transitionnetwork.org/about>. Walker, B. H., and David Salt. Resilience Thinking: Sustaining Ecosystems and People in a Changing World. Island Press, 2006. Walker, Brian et al. “Resilience, Adaptability and Transformability in Social–Ecological Systems.” Ecology and Society 9.2 (2004): 5. Wasdell, David. “A Topological Approach.” The Feedback Crisis in Climate Change: The Meridian Report. n.d. 16 Aug. 2013 ‹http://www.meridian.org.uk/Resources/Global%20Dynamics/Feedback%20Crisis/frameset1.htm?p=3>. ———. “Beyond the Tipping Point: Positive Feedback and the Acceleration of Climate Change.” The Foundation for the Future, Humanity 3000 Workshop. Seattle, 2006. ‹http://www.meridian.org.uk/_PDFs/BeyondTippingPoint.pdf>. ———. “Feedback Dynamics and the Acceleration of Climate Change.” Winterthur, 2008. 16 Aug. 2013 ‹http://www.crisis-forum.org.uk/events/Workshop1/Workshop1_presentations/wasdellpictures/wasdell_clubofrome.php>. Werner, Emmy E., Jessie M. Bierman, and Fern E. French. The Children of Kauai: A Longitudinal Study from the Prenatal Period to Age Ten. University of Hawaii Press, 1971.WGBH. “Bridge Basics.” Building Big. 2001. 14 Aug. 2013 ‹http://www.pbs.org/wgbh/buildingbig/bridge/basics.html>. Wikipedia contributors. “Gravitron.” Wikipedia, the Free Encyclopedia 20 Sep. 2013. 25 Sep. 2013 ‹http://en.wikipedia.org/wiki/Gravitron>. ———. “Hooke’s Law.” Wikipedia, the Free Encyclopedia 8 Aug. 2013. 15 Aug. 2013 ‹http://en.wikipedia.org/wiki/Hooke%27s_law>. ———. “Spring (device).” Wikipedia, the Free Encyclopedia 9 Aug. 2013. 24 Sep. 2013 ‹http://en.wikipedia.org/wiki/Spring_(device)>. ———. “System Dynamics.” Wikipedia, the Free Encyclopedia 9 Aug. 2013. 13 Aug. 2013 ‹http://en.wikipedia.org/wiki/System_dynamics>.