Relevant bibliographies by topics / Peridynamics

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
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Academic literature on the topic 'Peridynamics'

Author: Grafiati
Published: 4 June 2021
Last updated: 6 September 2023

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Journal articles on the topic "Peridynamics"

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Huang, Zaixing. "Noether’s theorem in peridynamics." Mathematics and Mechanics of Solids 24, no. 11 (November 12, 2018): 3394–402. http://dx.doi.org/10.1177/1081286518812931.

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By introducing a new nonlocal argument, the Lagrangian formulation of peridynamics is investigated. The peridynamic Euler–Lagrange equation is derived from Hamilton’s principle, and Noether’s theorem is extended into peridynamics. With the help of the peridynamic Noether’s theorem, the conservation laws relevant to energy, linear momentum, angular momentum and the Eshelby integral are determined. The results show that the peridynamic conservation laws exist only in a spatial integral form rather than in a pointwise form due to nonlocality. In bond-based peridynamics, energy conservation requires that the influence function is independent of the relative displacement field, or energy dissipation will occur. In state-based peridynamics, the angular momentum conservation causes a constraint on the constitutive relation between the force vector-state and the deformation vector-state. The Eshelby integral of peridynamics is given, which can be used to judge nucleation of defects and to calculate the energy release rates caused by damage, fracture and phase transition.
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Yu, Ming, Zeyuan Zhou, and Zaixing Huang. "Traction-Associated Peridynamic Motion Equation and Its Verification in the Plane Stress and Fracture Problems." Materials 16, no. 6 (March 10, 2023): 2252. http://dx.doi.org/10.3390/ma16062252.

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How to prescribe traction on boundary surface is still an open question in peridynamics. This problem is investigated in this paper. Through introducing the induced body force defined by boundary traction, the Silling’s peridynamic motion equation is extended to a new formulation called the traction-associated peridynamic motion equation, which is verified to be compatible with the conservation laws of linear momentum and angular momentum. The energy conservation equation derived from the traction-associated peridynamic motion equation has the same form as that in the original peridynamics advanced by Silling. Therefore, the constitutive models of the original peridynamics can be directly applied to the traction-associated peridynamic motion equation. Some benchmark examples in the plane stress problems are calculated. The numerical solutions agree well with the classical elasticity solutions, and the volume correction and the surface correction are no longer needed in the numerical algorithm. These results show that the traction-associated peridynamic motion equation not only retains all advantages of the original peridynamics, but also can conveniently deal with the complex traction boundary conditions.
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Yaghoobi, Amin, and Mi G. Chorzepa. "Formulation of symmetry boundary modeling in non-ordinary state-based peridynamics and coupling with finite element analysis." Mathematics and Mechanics of Solids 23, no. 8 (June 12, 2017): 1156–76. http://dx.doi.org/10.1177/1081286517711495.

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Peridynamics is an effective method in computational solid mechanics for dealing with discontinuities. However, its computational cost limits its applications, especially when used in the most general form, non-ordinary state-based peridynamics. This paper considers two approaches which decrease the computational cost. The first approach accounts for symmetry boundary conditions in a peridynamic body. In nonlocal peridynamics, boundary conditions are applied to an area. Therefore, when modeling the symmetry boundary condition, assuming fixed particles around the symmetry axis yields incorrect results. The present formulation introduces constraints which allow modeling of local symmetry conditions. Second, the finite-element–peridynamic coupling method is adopted for non-ordinary state-based peridynamics. The coupling method enables the use of peridynamics around discontinuities like cracks, and the faster finite element for the surrounding body. These two methods effectively reduce the solution time with an acceptable accuracy. The validity of these approaches is studied through various examples. Also, ductile crack growth in a compact tension specimen is studied, applying the presented methods. Good agreement is found when comparing experimental results with corresponding numerical results obtained using either fully peridynamic or coupled models.
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Nishawala, Vinesh V., and Martin Ostoja-Starzewski. "Peristatic solutions for finite one- and two-dimensional systems." Mathematics and Mechanics of Solids 22, no. 8 (April 21, 2016): 1639–53. http://dx.doi.org/10.1177/1081286516641180.

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Peridynamics is a nonlocal continuum mechanics theory where its governing equation has an integro-differential form. This paper specifically uses bond-based peridynamics. Typically, peridynamic problems are solved via numerical means, and analytical solutions are not as common. This paper analytically evaluates peristatics, the static version of peridynamics, for a finite one-dimensional rod as well as a special case for two dimensions. A numerical method is also implemented to confirm the analytical results.
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Shen, Feng, Qing Zhang, and Dan Huang. "Damage and Failure Process of Concrete Structure under Uniaxial Compression Based on Peridynamics Modeling." Mathematical Problems in Engineering 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/631074.

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Peridynamics is a nonlocal formulation of continuum mechanics, which uses integral formulation rather than the spatial partial differential equations. The peridynamic approach avoids using any spatial derivatives, which arise naturally in the classical local theory. It has shown effectiveness and advantage in solving discontinuous problems at both macro- and microscales. In this paper, the peridynamic theory is used to analyze damage and progressive failure of concrete structures. A nonlocal peridynamic model for concrete columns under uniaxial compression is developed. Numerical example illustrates that cracks in a peridynamic body of concrete form spontaneously. The result of the example clarifies the unique advantage of modeling damage accumulation and progressive failure of concrete based on peridynamic theory. This study provides a new promising alternative for analyzing complicated discontinuity problems. Finally, some open problems and future research trends in peridynamics are discussed.
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Friebertshäuser, Kai, Christian Wieners, and Kerstin Weinberg. "Dynamic fracture with continuum-kinematics-based peridynamics." AIMS Materials Science 9, no. 6 (2022): 791–807. http://dx.doi.org/10.3934/matersci.2022049.

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<abstract><p>This contribution presents a concept to dynamic fracture with continuum-kinematics-based peridynamics. Continuum-kinematics-based peridynamics is a geometrically exact formulation of peridynamics, which adds surface- or volume-based interactions to the classical peridynamic bonds, thus capturing the finite deformation kinematics correctly. The surfaces and volumes considered for these non-local interactions are constructed using the point families derived from the material points' horizon. For fracture, the classical bond-stretch damage approach is not sufficient in continuum-kinematics-based peridynamics. Therefore it is here extended to the surface- and volume-based interactions by additional failure variables considering the loss of strength in the material points' internal force densities. By numerical examples, it is shown that the presented approach can correctly handle crack growth, impact damage, and spontaneous crack initiation under dynamic loading conditions with large deformations.</p></abstract>
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Chen, Jingkai, Ye Tian, and Xuezheng Cui. "Free and Forced Vibration Analysis of Peridynamic Finite Bar." International Journal of Applied Mechanics 10, no. 01 (January 2018): 1850003. http://dx.doi.org/10.1142/s1758825118500035.

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Peridynamics is a reformulated nonlocal elasticity theory. Unlike the local elasticity theory, the peridynamics is proposed with no continuum assumption. In this paper, a new analytical approach to analyze the vibration of peridynamic finite bar with specified boundary condition is proposed. It is proved that the nonlocal dispersive relation of the peridynamic bar is nonlinear and can be reduced to the local dispersive relation when the peridynamic horizon goes to zero. The phase velocity, as a function of the wave frequency, is proved to be positive and asymptotically decreasing. The homogenous and the nonhomogeneous solutions of the peridynamic bar vibration equation are derived analytically by using the separation of variables. The mode shape characteristic equation of peridynamic bar, which is a second kind Fredholm integral equation, is expanded with a Taylor series expansion up to the infinite order; the corresponding mode shape is derived by solving a differential equation up to the infinite order. The peridynamic boundary condition is analyzed and compared with the local boundary condition. The numerical modeling based on mesh-free method verifies the analytical results for both free vibration and forced vibration cases.
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Liu, Shankun, Fei Han, Xiaoliang Deng, and Ye Lin. "Thermomechanical Peridynamic Modeling for Ductile Fracture." Materials 16, no. 11 (May 30, 2023): 4074. http://dx.doi.org/10.3390/ma16114074.

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In this paper, we propose a modeling method based on peridynamics for ductile fracture at high temperatures. We use a thermoelastic coupling model combining peridynamics and classical continuum mechanics to limit peridynamics calculations to the failure region of a given structure, thereby reducing computational costs. Additionally, we develop a plastic constitutive model of peridynamic bonds to capture the process of ductile fracture in the structure. Furthermore, we introduce an iterative algorithm for ductile-fracture calculations. We present several numerical examples illustrating the performance of our approach. More specifically, we simulated the fracture processes of a superalloy structure in 800 ℃ and 900 ℃ environments and compared the results with experimental data. Our comparisons show that the crack modes captured by the proposed model are similar to the experimental observations, verfying the validity of the proposed model.
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Freimanis, Andris, and Sakdirat Kaewunruen. "Peridynamic Analysis of Rail Squats." Applied Sciences 8, no. 11 (November 19, 2018): 2299. http://dx.doi.org/10.3390/app8112299.

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Rail surface defects are a serious concern for railway infrastructure managers all around the world. They lead to poor ride quality due to excess vibration and noise; in rare cases, they can result in a broken rail and a train derailment. Defects are typically classified as ‘rail studs’ when they initiate from the white etching layer, and ‘rail squats’ when they initiate from rolling contact fatigue. This paper presents a novel investigation into rail squat initiation and growth simulations using peridynamic theory. To the best of the authors’ knowledge, no other comprehensive study of rail squats has been carried out using this approach. Peridynamics are well-suited for fracture problems, because, contrary to continuum mechanics, they do not use partial-differential equations. Instead, peridynamics use integral equations that are defined even when discontinuities (cracks, etc.) are present in the displacement field. In this study, a novel application of peridynamics to rail squats is verified against a finite element solution, and the obtained simulation results are compared with in situ rail squat measurements. Some new insights can be drawn from the results. The outcome exhibits that the simulated cracks initiate and grow unsymmetrically, as expected and reported in the field. Based on this new insight, it is apparent that peridynamic modelling is well-applicable to fatigue crack modeling in rails. Surprisingly, limitations to the peridynamic analysis code have also been discovered. Future work requires finding an adequate solution to the matter-interpenetration problem.
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Altenbach, Holm, Oleksiy Larin, Konstantin Naumenko, Olha Sukhanova, and Mathias Würkner. "Elastic plate under low velocity impact: Classical continuum mechanics vs peridynamics analysis." AIMS Materials Science 9, no. 5 (2022): 702–18. http://dx.doi.org/10.3934/matersci.2022043.

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<abstract><p>The aim of this paper is to compare the classical continuum mechanics and the peridynamic models in the structural analysis of a monolithic glass plate subjected to ball drop. Governing equations are recalled in order to highlight the differences and basic features of both approaches. In this study the behavior of glass is assumed to be linear-elastic and damage processes are ignored. The generalized Hooke's law is assumed within the classical theory, while the linear peridynamic solid constitutive model is applied within the peridynamic analysis. Mechanical models for the ball drop simulation are discussed in detail. An emphasis is placed on the discretization including finite element mesh, peridynamic node lattice and time stepping, as well as appropriate constraints and contact conditions in both finite element and non-local peridynamics models. Deflections of the plate after the ball drop are presented as functions of time and the results based on the finite element and peridynamic analysis are compared. Good agreements between the deflection values in selected points of the plate as well as deflection fields at several time points indicate, that the model assumptions for the non-local peridynamic analysis including the horizon size, the short-range force contact settings and the support conditions are well suited. The developed peridynamics models can be applied in the future to analyze damage patterns in glass plates.</p></abstract>
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Dissertations / Theses on the topic "Peridynamics"

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Degl'Incerti, Tocci Corrado. "Analysis of Composites using Peridynamics." Thesis, Virginia Tech, 2014. http://hdl.handle.net/10919/25351.

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Since the last century a lot of effort has been spent trying to analyze damage and crack evolution in solids. This field is of interest because of the many applications that require the study of the behavior of materials at the micro- or nanoscale, i.e. modeling of composites and advanced aerospace applications. Peridynamics is a recently developed theory that substitutes the differential equations that constitute classical continuum mechanics with integral equations. Since integral equations are valid at discontinuities and cracks, peridynamics is able to model fracture and damage in a more natural way, without having to work around mathematical singularities present in the classical continuum mechanics theory. The objective of the present work is to show how peridynamics can be implemented in finite element analysis (FEA) using a mesh of one-dimensional truss elements instead of 2-D surface elements. The truss elements can be taken as a representation of the bonds between molecules or particles in the body and their strength is found according to the physical properties of the material. The possibility implementing peridynamics in a finite element framework, the most used method for structural analysis, is critical for expanding the range of problems that can be analyzed, simplifying the verification of the code and for making fracture analysis computationally cheaper. The creation of an in-house code allows for easier modifications, customization and enrichment if more complex cases (such as multiscale modeling of composites or piezoresistive materials) are to be analyzed. The problems discussed in the present thesis involve plates with holes and inclusions subjected to tension. Displacement boundary conditions are applied in all cases. The results show good agreement with theory as well as with empirical observation. Stress concentrations reflect the behavior of materials in real life, cracks spontaneously initiate and debonding naturally happens at the right locations. Several examples clearly show this behavior and prove that peridynamics is a promising tool for stress and fracture analysis.
Master of Science
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Diyaroglu, Cagan. "Peridynamics and its applications in marine structures." Thesis, University of Strathclyde, 2016. http://oleg.lib.strath.ac.uk:80/R/?func=dbin-jump-full&object_id=26573.

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Prediction of fracture and failure is a challenging research area. There are various methods available in the literature for this purpose including well-known finite element (FE) method. FE method is a powerful technique for deformation and stress analysis of structures. However, it has various disadvantageous in predicting failure due to its mathematical structure since it is based on classical continuum mechanics (CCM). CCM has governing equations in the form of partial differential equations. These equations are not valid if the displacement field is discontinuous as a result of crack occurance. In order to overcome this problem, a new continuum mechanics formulation was introduced and named as Peridynamics. Peridynamics uses integrals equations as opposed to partial differential equations of CCM. Moreover, it does not contain any spatial derivatives. Hence, its equations are always valid regardless of discontinuities. In this thesis, the applications of Peridynamics for marine structues are demonstrated. Particularly, the Peridynamic equations are rederived for simplified structures commonly used in marine structures including beams and plates. Furthermore, underwater shock response of marine composites is investigated. Finally, the peridynamic formulation for contact analysis which can be used for collision and grounding of ship structures is demonstrated. In order to reduce the computational time, several solution strategies are explained.
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Oterkus, Selda. "Peridynamics For The Solution Of Multiphysics Problems." Diss., The University of Arizona, 2015. http://hdl.handle.net/10150/555945.

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This study presents peridynamic field equations for mechanical deformation, thermal diffusion, moisture diffusion, electric potential distribution, porous flow and atomic diffusion in either an uncoupled or a coupled manner. It is a nonlocal theory with an internal length parameter. Therefore, it can capture physical phenomenon for the problems which include non-local effects and are not suitable for classical theories. Moreover, governing equations of peridynamics are based on integro-differential equations which permits the determination of the field variable in spite of discontinuities. Inherent with the nonlocal formulations, the imposition of the boundary conditions requires volume constraints. This study also describes the implementation of the essential and natural boundary conditions, and demonstrates the accuracy of their implementation. Solutions coupled field problems concerning plastic deformations, thermomechanics, hygrothermomechanics, hydraulic fracturing, thermal cracking of fuel pellet and electromigration are constructed. Their comparisons with the finite element predictions establish the validity of the PD field equations for coupled field analysis.
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Bazazzadeh, Soheil. "Discontinuous mechanical problems studied with a Peridynamics-based approach." Doctoral thesis, Università degli studi di Padova, 2018. http://hdl.handle.net/11577/3425762.

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The classical theory of solid mechanics is rooted in the assumption of a continuous distribution of mass within a body. It employs partial differential equations (PDEs) with significant smoothness to obtain displacements and internal forces of the body. Although classical theory has been applied to wide range of engineering problems, PDEs of the classical theory cannot be applied directly on a discontinuity such as cracks. Peridynamics is considered to be an alternative and promising nonlocal theory of solid mechanics that, by replacing PDEs of classical theory with integral or integro-differential equations, attempts to unite the mathematical modelling of continuous media, cracks and particles within a single framework. Indeed, the equations of peridynamic are based on the direct interaction of material points over finite distances. Another concept, derived from the peridynamic approach to cope with engineering problems with discontinuities, is that of the peridynamic differential operator (PDDO). The PDDO uses the non-local interaction of the material points in a way similar to that of peridynamics. PDDO is capable to recast partial derivatives of a function through a nonlocal integral operator whose kernel is free of using any correction function. In this dissertation, application of peridaynamics and PDDO, to three different important engineering problems including fatigue fracture, thermo-mechanics and sloshing phenomena, is examined comprehensively. To cope with fatigue fracture problems, an algorithm has been developed in such a way that the increment of damage due to fatigue is added to that due to the static increment of the opening displacement. A one degree of freedom cylinder model has been used to carry out an efficient comparison of the computational performance of three fatigue degradation strategies. The three laws have been implemented in a code using bond based peridynamics (BBPD) to simulate fatigue crack propagation. Both the cylinder model and the bond base peridynamics code provide the same assessment of the three fatigue degradation strategies. To deal with thermo-mechanical problems, an effective way is proposed to use a variable grid size in a weakly coupled thermal shock peridynamic model. The proposed numerical method is equipped with stretch control criterion to transform the grid discretization adaptively in time. Hence, finer grid spacing is only applied in limited zones where it is required. This method is capable of predicting complex crack patterns in the model. By introducing fine grid discretization over the boundaries of the model the surface (softening) effect can be reduced. The accuracy and performance of the model are examined through problems such as thermo-elastic and thermal-shock induced fracture in ceramics. Finally to investigate sloshing phenomena, the PDDO has been applied to the solution of problems of liquid sloshing in 2D and 3D tanks with potential flow theory and Lagrangian description. Moreover, liquid sloshing in rectangular tanks containing horizontal and vertical baffles are investigated to examine the robustness and accuracy of PDDO. With respect to other approaches such as meshless local Petrov-Galerkin (MLPG), volume of fluid (VOF) and and local polynomial collocation methods the examples are solved with a coarser grid of nodes. Using this new approach, one is able to obtain results with a high accuracy and low computational cost.
La teoria classica della meccanica dei solidi, formulata tramite equazioni differenziali alle derivate parziali (PDEs), è basata sull'assunzione di una distribuzione continua di massa all'interno di un corpo. Sebbene la teoria classica sia stata applicata ad un'ampia gamma di problemi ingegneristici, le equazioni differenziali su cui è basata non possono essere risolte agevolmente in presenza di una discontinuità come, ad es., una cricca. La peridinamica è considerata un'alternativa ed una promettente teoria non-locale della meccanica dei solidi che, rimpiazzando le equazioni differenziali con equazioni integrali o integro-differenziali, unisce in un’unica formulazione la modellazione dei solidi continui e quella di discontinuità (ad es. cricche). Le equazioni della peridinamica sono basate sull'interazione diretta di punti materiali all’interno di una regione di influenza di dimensioni finite. Un altro concetto, derivato dall'approccio peridinamico è l'operatore differenziale peridinamico (PDDO). Questo operatore è in grado di valutare le derivate parziali di una generica funzione per mezzo di una opportuna funzione integrale non-locale. In questa tesi viene esaminata l'applicazione della peridinamica e del PDDO a tre problemi ingegneristici: la frattura per fatica, i fenomeni termo-meccanici ed i fenomeni di sloshing. Per simulare i problemi di frattura per fatica, è stato sviluppato un algoritmo che valuta sia l'incremento del danno per fatica, legato al numero dei cicli di carico, che l’incremento del danno statico, legato all’aumento dell’apertura della cricca. Sono state proposte tre leggi di danneggiamento per fatica le cui prestazioni computazionali sono state valutate per mezzo di un modello ad un grado di libertà. Inoltre le stesse tre leggi sono state implementate in un codice basato sulla formulazione peridinamica di tipo bond-based, per simulare la propagazione delle cricche per fatica. Sia il modello ad un grado di libertà che il codice scritto utilizzando la formulazione peridinamica individuano la stessa legge di danneggiamento per fatica (fra le 3 studiate) quale più efficiente ed accurata da un punto di vista numerico. Per affrontare problemi di natura termo-meccanica, viene proposto un approccio alternativo che utilizza una griglia di nodi di dimensione variabile all’interno di un modello peridinamico. Il modello numerico proposto modifica in maniera adattiva la dimensione di griglia per garantire una elevata accuratezza dei risultati ed un minore sforzo computazionale: la griglia più raffinata è usata soltanto nelle aree in cui le cricche si propagano. L’approccio proposto è stato utilizzato in un primo momento per lo studio di fenomeni termo-elastici quindi per l’analisi di fenomeni di propagazione di cricche a seguito di sollecitazioni termo-meccaniche. Infine, il PDDO è stato impiegato per investigare i fenomeni di sloshing di liquidi in serbatoi bi-dimensionali e tri-dimensionali studiati con la teoria del flusso a potenziale e la descrizione Lagrangiana. Rispetto ad altri approcci, come ad esempio il metodo locale meshless Petrov-Galarkin, il metodo dei volumi di fluido ed il metodo locale di collocazione polinomiale, l’approccio PDDO si rivela particolarmente efficace dato che fornisce risultati di accuratezza analoga (rispetto ai risultati ottenuti con gli altri approcci) impiegando un numero minore di nodi per descrivere il sistema.
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Kilic, Bahattin. "Peridynamic Theory for Progressive Failure Prediction in Homogeneous and Heterogeneous Materials." Diss., The University of Arizona, 2008. http://hdl.handle.net/10150/193658.

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The classical continuum theory is not capable of predicting failure without an external crack growth criteria and treats the interface having zero thickness. Alternatively, a nonlocal continuum theory referred to as peridynamic theory eliminates these shortcomings by utilizing formulation that uses displacements, rather than derivatives of displacements, and including material failure in its constitutive relations through the response functions. This study presents a new response function as part of the peridynamic theory to include thermal loading. Furthermore, an efficient numerical algorithm is presented for solution of peridynamic equations. Solution method relies on the discretization of peridynamic equations at collocation points resulting in a set of ordinary differential equations with respect to time. These differential equations are then integrated using explicit methods. In order to improve numerical efficiency of the computations, spatial partitioning is introduced through uniform grids as arrays of linked lists. Furthermore, the domain of interest is divided into subunits each of which is assigned to a specific processor to utilize parallel processing using OpenMP. In order to obtain the static solutions, the adaptive dynamic relaxation method is developed for the solution of peridynamic equations. Furthermore, an approach to couple peridynamic theory and finite element analysis is introduced to take advantage of their salient features. The regions in which failure is expected are modeled using peridynamics while the remaining regions are modeled utilizing finite element method. Finally, the present solution method is utilized for damage prediction of many problems subjected to mechanical, thermal and buckling loads.
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Dipasquale, Daniele. "Adaptive Grid Refinement and Scaling Techniques Applied to Peridynamics." Doctoral thesis, Università degli studi di Padova, 2017. http://hdl.handle.net/11577/3426213.

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Peridynamics, a recently proposed non-local continuum theory, is particularly suitable to describe fracture phenomena in a wide range of materials. One of most common techniques for its numerical implementation is based on a mesh-free approach, in which the whole body is discretized with a uniform grid and a constant horizon, the latter related to the length-scale of the material and/or of the phenomenon analysed. As a consequence of that, computational resources may not be used efficiently. The present work proposes adaptive refinement/scaling algorithms for 2D and 3D peridynamic grids, to reduce the computational cost of peridynamic based software. Adaptive refinement/scaling is here applied to the study of dynamic crack propagation in brittle materials. Refinement is activated by using a new trigger concept based on the damage state of the material, coupled with the more traditional energy based trigger, already proposed in the literature. The use of a varying horizon and grid spacing over the grid may introduce some anomalies on the numerical peridynamic solution, such anomalies are investigated in detail through static and dynamic analyses. Moreover, while the scientific community is working to assess the full potential of peridynamics, few researchers have observed indirectly that the evolution of crack paths can follow, in an unphysical way, the axes of symmetry of the grid. The main parameter affecting such a numerical phenomenon seems to be the value of the m ratio, namely the ratio between the horizon and the grid spacing. The dependence of the crack path on the grid orientation would be a serious drawback for peridynamic based software since it would undermine what is believed to be one of its most important advantages over other computational methods, i.e. its capability to simulate (multiple) crack nucleation, propagation, branching and interaction in solids in a simple way. Finally, in order to show the effectiveness of the proposed approach, several examples of crack propagation in both 2D and 3D problems are presented. Then, the results obtained are compared with those obtained with other numerical methods and with experimental data.
La Peridynamica, una teoria non locale del continuo proposta recentemente, è particolarmente adatta a descrivere fenomeni di frattura in una vasta gamma di materiali. Una delle tecniche più comuni per la sua implementazione numerica è basata su un approccio senza mesh, in cui l'intero corpo viene discretizzato con una griglia uniforme e un orizzonte costante, essendo quest'ultimo in relazione con la lunghezza di scala del materiale e/o del fenomeno analizzato. Di conseguenza le risorse computazionali possono non essere utilizzate in modo efficiente. Il presente lavoro si propone di sviluppare gli algoritmi per l’implementazione dell’adaptive grid refinement and scaling per griglie peridinamiche 2D e 3D, con lo scopo di ridurre il costo computazionale dei software basati sulla peridynamica. Questo approccio viene applicato allo studio della propagazione dinamica di cricche in materiali fragili. Il refinement viene attivato utilizzando un nuovo concetto di “innesco” che si basa sullo stato di danneggiamento del materiale, accoppiato con il più tradizionale innesco basato su un criterio energetico, già proposto in letteratura. L' utilizzo di un orizzonte e di un passo di griglia variabile può introdurre nella soluzione numerica della peridynamica alcune anomalie, che vengono analizzate dettagliatamente tramite analisi statiche e dinamiche. Inoltre, mentre la maggior parte della comunità scientifica sta lavorando per valutare a pieno le potenzialità della peridynamica, solo alcuni ricercatori hanno osservato indirettamente come il percorso della cricca possa seguire, in modo chiaramente non realistico, gli assi di simmetria della griglia. Il principale parametro che influisce su tale comportamento sembra essere il valore assunto dal rapporto m, definito come il rapporto tra l'orizzonte e il passo della griglia. La dipendenza del percorso della cricca dall'orientamento della griglia sarebbe un grave ostacolo per lo sviluppo di un software basato sulla peridynamica, poiché ciò porterebbe a pregiudicare quella che si ritiene essere uno dei suoi vantaggi più importanti rispetto ad altri metodi di calcolo, ossia la sua capacità di simulare la nucleazione (anche multipla), la propagazione, la ramificazione e l’interazione di cricche in materiali solidi in modo semplice. Successivamente, al fine di dimostrare l'efficacia del metodo proposto, vengono presentati alcuni esempi di propagazione di cricche per problemi 2D e 3D. Infine, i risultati ottenuti sono confrontati con quelli ottenuti con altri metodi numerici e con dati sperimentali.
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Bang, Dongjun. "Peridynamic Modeling of Hyperelastic Materials." Diss., The University of Arizona, 2016. http://hdl.handle.net/10150/595809.

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This study concerns the development of the peridynamic strain energy density function for a Neo-Hookean type membrane under equibiaxial, planar and uniaxial loading conditions. The material parameters for each loading case are determined by equating the peridynamic strain energy to those of the classical continuum mechanics. Therefore, the peridynamic equations of motion are derived based on the Neo-Hookean model under the assumption of incompressibility. Numerical results concern the deformation of a membrane without and with a defect in the form of a hole, an inclusion and a crack under equibiaxial, planar and uniaxial loading conditions. As part of the verification process, the peridynamic predictions are compared with those of finite element analysis. For all defect types and loading conditions, the comparisons indicate excellent agreement.
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Sadat, Mohammad Rafat, and Mohammad Rafat Sadat. "Using Molecular Dynamics and Peridynamics Simulations to Better Understand Geopolymer." Diss., The University of Arizona, 2017. http://hdl.handle.net/10150/626361.

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Geopolymer is a novel cementitious material which can be a potential alternative to ordinary Portland cement (OPC) for all practical applications. However, until now research on this revolutionary material is limited mainly to experimental studies, which have the limitations in considering the details of the atomic- and meso-scale structure and atomic scale mechanisms that govern the properties at the macro-scale. Most experimental studies on geopolymer have been conducted focusing only on the macroscopic properties and considering it as a single-phase material. However, research has shown that geopolymer is a composite material consisting of geopolymer binder (GB), unreacted source material, and, in the presence of Ca in the source material, calcium silicate hydrate (CSH). Therefore, in this research, a multiscale/multiphysics modeling approach has been taken to understand geopolymer structure and mechanical properties under varying conditions and at different length scales. First, GB was prepared at the atomic scale using molecular dynamics (MD) simulations with varying Si/Al ratios and water contents within the nano voids. The MD simulated geopolymer structure was validated based on comparison with experiments using X-ray pair distribution function (PDF), infra-red (IR) spectra, coordination of atoms, and density. The results indicate that the highest strength occurs at a Si/Al ratio of 2-3 and the presence of molecular water negatively affects the mechanical properties of GB. The loss of strength for GB with increased water content is linked to the diffusion of Na atoms and subsequent weakening of Al tetrahedra. The GB was also subjected to nanoindentation using MD and the effect of indenter size and loading rate was investigated at an atomic scale. A clear correlation between the indenter size and observed hardness of GB was observed which proves indentation size effects (ISE). Realizing the composite nature of geopolymer, the presence of unreacted and secondary phases such as quartz and CSH in geopolymer was also investigated. To do that, the mechanical properties of GB, the secondary phases and their interfaces was first determined from MD simulations. Using the MD generated properties, a meso-scale model of geopolymer composite was prepared in Peridynamics (PD) framework which considered large particles of GB and secondary phases of nanometers in size which cannot be easily modeled in MD. The meso-scale model provides a larger platform to study geopolymer in the presence of large nano-voids and multiple phases. Results from the PD simulations were directly comparable to experimentally observed mechanical properties. Findings of this study can be directly used in future to construct more advanced and sophisticated models of geopolymer and will be instrumental in designing the synthesis condition for geopolymer with superior mechanical properties.
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Glaws, Andrew Taylor. "Finite Element Simulations of Two Dimensional Peridynamic Models." Thesis, Virginia Tech, 2014. http://hdl.handle.net/10919/48121.

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This thesis explores the science of solid mechanics via the theory of peridynamics. Peridynamics has several key advantages over the classical theory of elasticity. The most notable of which is the ease with which fractures in the the material are handled. The goal here is to study the two theories and how they relate for problems in which the classical method is known to work well. While it is known that state-based peridynamic models agree with classical elasticity as the horizon radius vanishes, similar results for bond-based models have yet to be developed. In this study, we use numerical simulations to investigate the behavior of bond-based peridynamic models under this limit for a number of cases where analytic solutions of the classical elasticity problem are known. To carry out this study, the integral-based peridynamic model is solved using the finite element method in two dimensions and compared against solutions using the classical approach.
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Colavito, Kyle Wesley. "Peridynamics for Failure and Residual Strength Prediction of Fiber-Reinforced Composites." Diss., The University of Arizona, 2013. http://hdl.handle.net/10150/311300.

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Peridynamics is a reformulation of classical continuum mechanics that utilizes integral equations in place of partial differential equations to remove the difficulty in handling discontinuities, such as cracks or interfaces, within a body. Damage is included within the constitutive model; initiation and propagation can occur without resorting to special crack growth criteria necessary in other commonly utilized approaches. Predicting damage and residual strengths of composite materials involves capturing complex, distinct and progressive failure modes. The peridynamic laminate theory correctly predicts the load redistribution in general laminate layups in the presence of complex failure modes through the use of multiple interaction types.This study presents two approaches to obtain the critical peridynamic failure parameters necessary to capture the residual strength of a composite structure. The validity of both approaches is first demonstrated by considering the residual strength of isotropic materials. The peridynamic theory is used to predict the crack growth and final failure load in both a diagonally loaded square plate with a center crack, as well as a four-point shear specimen subjected to asymmetric loading.This study also establishes the validity of each approach by considering composite laminate specimens in which each failure mode is isolated. Finally, the failure loads and final failure modes are predicted in a laminate with various hole diameters subjected to tensile and compressive loads.
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Books on the topic "Peridynamics"

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Rabczuk, Timon, Huilong Ren, and Xiaoying Zhuang. Computational Methods Based on Peridynamics and Nonlocal Operators. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-20906-2.

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Gerstle, Walter. Introduction to practical peridynamics: Computational solid mechanics without stress and strain. New Jersey: World Scientific, 2016.

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Madenci, Erdogan, and Erkan Oterkus. Peridynamic Theory and Its Applications. New York, NY: Springer New York, 2014. http://dx.doi.org/10.1007/978-1-4614-8465-3.

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Madenci, Erdogan, Atila Barut, and Mehmet Dorduncu. Peridynamic Differential Operator for Numerical Analysis. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-02647-9.

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Roy, Pranesh, Deepak Behera, and Erdogan Madenci. Advances in Peridynamics. Springer International Publishing AG, 2022.

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Ren, Huilong, Timon Rabczuk, and Xiaoying Zhuang. 'Computational Methods Based on Peridynamics and Nonlocal Operators: Theory and Applications. Springer International Publishing AG, 2023.

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T, Foster John, Florin Bobaru, Philippe H. Geubelle, and Stewart A. Silling. Handbook of Peridynamic Modeling. Taylor & Francis Group, 2016.

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T, Foster John, Florin Bobaru, Philippe H. Geubelle, and Stewart A. Silling. Handbook of Peridynamic Modeling. Taylor & Francis Group, 2016.

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Bobaru, Florin. Handbook of Peridynamic Modeling. Chapman and Hall/CRC, 2017. http://dx.doi.org/10.1201/9781315373331.

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Handbook of Peridynamic Modeling. Taylor & Francis Group, 2016.

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Book chapters on the topic "Peridynamics"

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Guven, Ibrahim. "Peridynamics." In Multiscale Paradigms in Integrated Computational Materials Science and Engineering, 219–47. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-24529-4_5.

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Weißenfels, Christian. "Peridynamics." In Simulation of Additive Manufacturing using Meshfree Methods, 125–38. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-87337-0_7.

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Silling, S. A. "Peridynamics: Introduction." In Handbook of Nonlocal Continuum Mechanics for Materials and Structures, 1–38. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-22977-5_29-1.

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Silling, S. A. "Peridynamics: Introduction." In Handbook of Nonlocal Continuum Mechanics for Materials and Structures, 1159–96. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-319-58729-5_29.

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Buryachenko, Valeriy A. "Bond-Based Peridynamics." In Local and Nonlocal Micromechanics of Heterogeneous Materials, 725–46. Cham: Springer International Publishing, 2012. http://dx.doi.org/10.1007/978-3-030-81784-8_16.

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Chen, Jingkai. "Peridynamics Beam Equation." In Nonlocal Euler–Bernoulli Beam Theories, 9–21. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-69788-4_3.

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Rabczuk, Timon, Huilong Ren, and Xiaoying Zhuang. "Dual-Horizon Peridynamics." In Computational Methods Based on Peridynamics and Nonlocal Operators, 25–66. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-20906-2_2.

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Madenci, Erdogan, Pranesh Roy, and Deepak Behera. "Correction to: Advances in Peridynamics." In Advances in Peridynamics, C1. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-97858-7_17.

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Madenci, Erdogan, Pranesh Roy, and Deepak Behera. "Peridynamic Modeling of Thermoelastic Deformation." In Advances in Peridynamics, 173–84. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-97858-7_8.

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Madenci, Erdogan, Pranesh Roy, and Deepak Behera. "Direct Imposition of Boundary Conditions without a Fictitious Layer." In Advances in Peridynamics, 145–72. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-97858-7_7.

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Conference papers on the topic "Peridynamics"

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Bartlett, John D., and Duane Storti. "A Single-Card GPU Implementation of Peridynamics." In ASME 2021 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/detc2021-68032.

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Abstract The rapid development of parallelization technology over the recent decades has provided a promising avenue for the acceleration of meshfree simulation methods. One such method, peridynamics, is particularly well-suited for parallelization due to the simplicity of the operations which must occur at each material point. However, while MPI-based parallelization (Message-Passing Interface; a method for CPU-based parallelization) of peridynamic problems is commonplace, GPU parallelization of peridynamics has received far less attention. While GPU technology may have once been an inferior option to MPI parallelization for peridynamics, modern GPU cards are more than capable of handling substantially sized peridynamics problems. This paper presents the parallelization of the peridynamic method for single-card GPU computing, providing a schematic for a compact parallel approach. The resulting method is tested with CUDA on a NVIDIA Tesla P100 card with 16 GB of memory. The per-node memory requirements for each data structure used are evaluated, as well as the per-node execution times for each operation in a million-node benchmark test. This setup is shown to provide speedup factors over 200 for problems sized up to several million nodes, therefore indicating such a GPU is more than adequate for the single-card parallelization of the peridynamic method.
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Kulkarni, Shank S., Alireza Tabarraei, and Xiaonan Wang. "Study of Spurious Wave Reflection at the Interface of Peridynamics and Finite Element Regions." In ASME 2018 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/imece2018-86129.

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Peridynamics ability to model crack as a material response removes deficiencies associated with using classical continuum-based methods in modeling discontinuities. Due to its nonlocal formulation, however, peridynamics is computationally more expensive than the classical continuum-based numerical methods such as finite element method. To reduce the computational cost, peridynamics can be coupled with finite element method. In this method, peridynamics is used only in critical areas such as the vicinity of crack tip and finite element method is used everywhere else. The main issue associated with such coupling methods is the spurious wave reflections occurring at the interface of peridynamics and finite elements. High frequency waves traveling from peridynamics to finite element spuriously reflect back at the interface and the amplitude of transmitted waves also alter. In this paper, we take an analytical approach to study this phenomenon of spurious reflections. We study the impact of factors such as horizon size of peridynamic formulation, discretization, and change in mesh size on the amplitude of spuriously reflected waves. Finally, we present a method to reduce these spurious reflections by using Arlequin method.
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Littlewood, David J. "Simulation of Dynamic Fracture Using Peridynamics, Finite Element Modeling, and Contact." In ASME 2010 International Mechanical Engineering Congress and Exposition. ASMEDC, 2010. http://dx.doi.org/10.1115/imece2010-40621.

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Peridynamics is a nonlocal extension of classical solid mechanics that allows for the modeling of bodies in which discontinuities occur spontaneously. Because the peridynamic expression for the balance of linear momentum does not contain spatial derivatives and is instead based on an integral equation, it is well suited for modeling phenomena involving spatial discontinuities such as crack formation and fracture. In this study, both peridynamics and classical finite element analysis are applied to simulate material response under dynamic blast loading conditions. A combined approach is utilized in which the portion of the simulation modeled with peridynamics interacts with the finite element portion of the model via a contact algorithm. The peridynamic portion of the analysis utilizes an elastic-plastic constitutive model with linear hardening. The peridynamic interface to the constitutive model is based on the calculation of an approximate deformation gradient, requiring the suppression of possible zero-energy modes. The classical finite element portion of the model utilizes a Johnson-Cook constitutive model. Simulation results are validated by direct comparison to expanding tube experiments. The coupled modeling approach successfully captures material response at the surface of the tube and the emerging fracture pattern.
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Dipasquale, Daniele, Erkan Oterkus, Giulia Sarego, Mirco Zaccariotto, and Ugo Galvanetto. "Refinement and Scaling Effects on Peridynamic Numerical Solutions." In ASME 2016 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/imece2016-67317.

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One of the most common methods to implement peridynamics numerically is based on the discretization of the whole body by means of a structured and regular grid of nodes and a constant horizon size. That leads to an inefficient use of computational resources as well as to the impossibility to explore the multi-scale capabilities of peridynamics within a unique framework. Adaptive grid refinement and scaling seem to be a promising strategy to reduce those limitations, allowing to increase the resolution of the analysis and to reach the interested length-scale only in the desired regions. The application of such an approach in the peridynamic solutions requires certainly to be investigated, in particular, this is done by the comparison of numerical peridynamic solutions with the analytical solutions of classic linear elasticity theory.
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Kulkarni, Shank S., Alireza Tabarraei, and Xiaonan Wang. "Modeling the Creep Damage of P91 Steel Using Peridynamics." In ASME 2019 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/imece2019-10069.

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Abstract Creep is an important failure mechanism of metal components working at a high temperature. To ensure the structural integrity and safety of systems working at high temperature it is essential to predict failure due to creep. Classical continuum based damage models are used widely for modeling creep damage. A more recently developed non-local mechanics formulation called peridynamics has displayed better performance in modeling damage with respect to classical local mechanics methods. In this paper, the peridynamic formulation is extended to model creep in metals. We have chosen Liu-Murakami creep model for developing a peridynamic formulation for modeling creep. The proposed formulation is validated by simulating creep tests for P91 steel and comparing the results with experimental data from the literature.
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Littlewood, David J. "A Nonlocal Approach to Modeling Crack Nucleation in AA 7075-T651." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-64236.

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A critical stage in microstructurally small fatigue crack growth in AA 7075-T651 is the nucleation of cracks originating in constituent particles into the matrix material. Previous work has focused on a geometric approach to modeling microstructurally small fatigue crack growth in which damage metrics derived from an elastic-viscoplastic constitutive model are used to predict the nucleation event [1, 2]. While a geometric approach based on classical finite elements was successful in explicitly modeling the polycrystalline grain structure, singularities at the crack tip necessitated the use of a nonlocal sampling approach to remove mesh size dependence. This study is an initial investigation of the peridynamic formulation of continuum mechanics as an alternative approach to modeling microstructurally small fatigue crack growth. Peridynamics, a nonlocal extension of continuum mechanics, is based on an integral formulation that remains valid in the presence of material discontinuities. To capture accurately the material response at the grain scale, a crystal elastic-viscoplastic constitutive model is adapted for use in non-ordinary state-based peridynamics through the use of a regularized deformation gradient. The peridynamic approach is demonstrated on a baseline model consisting of a hard elastic inclusion in a single crystal. Coupling the elastic-viscoplastic material model with peridynamics successfully facilitates the modeling of plastic deformation and damage accumulation in the vicinity of the particle inclusion. Lattice orientation is shown to have a strong influence on material response.
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Littlewood, David J., Kyran Mish, and Kendall Pierson. "Peridynamic Simulation of Damage Evolution for Structural Health Monitoring." In ASME 2012 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/imece2012-86400.

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Modal-based methods for structural health monitoring require the identification of characteristic frequencies associated with a structure’s primary modes of failure. A major difficulty is the extraction of damage-related frequency shifts from the large set of often benign frequency shifts observed experimentally. In this study, we apply peridynamics in combination with modal analysis for the prediction of characteristic frequency shifts throughout the damage evolution process. Peridynamics, a nonlocal extension of continuum mechanics, is unique in its ability to capture progressive material damage. The application of modal analysis to peridynamic models enables the tracking of structural modes and characteristic frequencies over the course of a simulation. Shifts in characteristic frequencies resulting from evolving structural damage can then be isolated and utilized in the analysis of frequency responses observed experimentally. We present a methodology for quasi-static peridynamic analyses, including the solution of the eigenvalue problem for identification of structural modes. Repeated solution of the eigenvalue problem over the course of a transient simulation yields a data set from which critical shifts in modal frequencies can be isolated. The application of peridynamics to modal analysis is demonstrated on the benchmark problem of a simply-supported beam. The computed natural frequencies of an undamaged beam are found to agree well with the classical local solution. Analyses in the presence of cracks of various lengths are shown to reveal frequency shifts associated with structural damage.
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Ha, Youn D., and Florin Bobaru. "Dynamic Brittle Fracture Captured With Peridynamics." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-65515.

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The bond-based peridynamic model is able to capture many of the essential characteristics of dynamic brittle fracture observed in experiments: crack branching, crack-path instability, asymmetries of crack paths, successive branching, secondary cracking at right angles from existing crack surfaces, etc. In this paper we investigate the influence of the stress waves on the crack branching angle and the velocity profile. We observe that crack branching in peridynamics evolves as the phenomenology proposed by the experimental evidence [1]: when a crack reaches a critical stage (macroscopically identified by its stress intensity factor) it splits into two or more branches, each propagating with the same speed as the parent crack, but with a much reduced process zone.
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Vasenkov, Alex V. "Stent Fracture Predictions With Peridynamics." In 2018 Design of Medical Devices Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/dmd2018-6866.

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Currently, stent therapy constitutes to over 95% of all endovascular interventions. The biological and clinical complications of stent therapy can now be well controlled with modern techniques and procedures. However, the mechanical failure of stent remains an important clinical problem [1]. While there is a consensus that such failure usually proceeds through mechanical fracture activation due to fatigue, the mechanisms of fracture activation are not well understood. The virtual analysis of fracture is typically conducted using the Finite Element Method (FEM) model regulated by the externally applied criteria of fracture nucleation. Typically, the FEM model must deal with ambiguity of derivatives of displacement at discontinuities and should contain requirements on mesh size to resolve material damage. In this study, we pursue an alternative approach, called peridynamics, to depict the mechanism of fracture activation. Peridynamic damage model does not require special criteria to guide crack or damage growth and naturally accounts for surface roughness that can highly influence fatigue life of stent.
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Madenci, Erdogan, Mehmet Dorduncu, Atila Barut, and Nam D. Phan. "Weak form of peridynamics." In 2018 AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2018. http://dx.doi.org/10.2514/6.2018-1223.

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Reports on the topic "Peridynamics"

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Unal, Cetin, and Hailong Chen. Modeling Metallic Fuel using Peridynamics. Office of Scientific and Technical Information (OSTI), May 2020. http://dx.doi.org/10.2172/1630837.

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Silling, Stewart Andrew. A coarsening method for linear peridynamics. Office of Scientific and Technical Information (OSTI), May 2010. http://dx.doi.org/10.2172/983676.

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Silling, Stewart A., and James V. Cox. Hierarchical multiscale method development for peridynamics. Office of Scientific and Technical Information (OSTI), October 2014. http://dx.doi.org/10.2172/1433068.

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Lehoucq, Richard B., Stewart Andrew Silling, Steven James Plimpton, and Michael L. Parks. Peridynamics with LAMMPS : a user guide. Office of Scientific and Technical Information (OSTI), January 2008. http://dx.doi.org/10.2172/959309.

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Lehoucq, Richard B., Stewart Andrew Silling, Pablo Seleson, Steven James Plimpton, and Michael L. Parks. Peridynamics with LAMMPS : a user guide. Office of Scientific and Technical Information (OSTI), November 2011. http://dx.doi.org/10.2172/1031301.

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Silling, Stewart Andrew, and Richard B. Lehoucq. Statistical coarse-graining of molecular dynamics into peridynamics. Office of Scientific and Technical Information (OSTI), October 2007. http://dx.doi.org/10.2172/922771.

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Mitchell, John Anthony. A nonlocal, ordinary, state-based plasticity model for peridynamics. Office of Scientific and Technical Information (OSTI), May 2011. http://dx.doi.org/10.2172/1018475.

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Gunzburger, Max. Mathematical and Numerical Analyses of Peridynamics for Multiscale Materials Modeling. Office of Scientific and Technical Information (OSTI), February 2015. http://dx.doi.org/10.2172/1170396.

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Hong, Jung-Wuk. Coupling of Peridynamics and Finite Element Formulation for Multiscale Simulations. Fort Belvoir, VA: Defense Technical Information Center, October 2012. http://dx.doi.org/10.21236/ada582696.

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Du, Qiang. Mathematical and Numerical Analyses of Peridynamics for Multiscale Materials Modeling. Office of Scientific and Technical Information (OSTI), November 2014. http://dx.doi.org/10.2172/1163672.

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