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Journal articles on the topic 'NONLINEAR STRAINS'

Author: Grafiati

Published: 11 September 2023

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1

Zhu, Haihui, Yanli Lin, Kelin Chen, and Zhubin He. "Forming Limit Analysis of Thin-Walled Extruded Aluminum Alloy Tubes under Nonlinear Loading Paths Using an Improved M-K Model." Materials 16, no. 4 (2023): 1647. http://dx.doi.org/10.3390/ma16041647.

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To meet the requirement of lighter weight and better performance in tube hydroforming, one of the most important tasks is to accurately predict the forming limit of thin-walled tubes under nonlinear loading paths. This work established the M-K+DF2012 model, a combination of the M-K model and the DF2012 ductile fracture criterion, for the forming limit prediction of thin-walled tubes under nonlinear loading paths. In this model, the failure of the groove is determined by the DF2012 criterion, and the corresponding strains in the uniform region are the limit strains. The limit strains of an AA60

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2

Morgan, Elise F., Oscar C. Yeh, Wesley C. Chang, and Tony M. Keaveny. "Nonlinear Behavior of Trabecular Bone at Small Strains." Journal of Biomechanical Engineering 123, no. 1 (2000): 1–9. http://dx.doi.org/10.1115/1.1338122.

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Study of the behavior of trabecular bone at strains below 0.40 percent is of clinical and biomechanical importance. The goal of this work was to characterize, with respect to anatomic site, loading mode, and apparent density, the subtle concave downward stress–strain nonlinearity that has been observed recently for trabecular bone at these strains. Using protocols designed to minimize end-artifacts, 155 cylindrical cores from human vertebrae, proximal tibiae, proximal femora, and bovine proximal tibiae were mechanically tested to yield at 0.50 percent strain per second in tension or compressio

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3

Guo, Minrui, Xiangwen Li, and Weizhong Xiao. "Combined Effects of the Tire Loading Velocity and the Nonlinear Cross-Anisotropic Properties of Granular Base on Critical Pavement Responses." Science of Advanced Materials 14, no. 1 (2022): 11–21. http://dx.doi.org/10.1166/sam.2022.4187.

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The primary purpose of the research is to explore the combined effects of the tire loading velocity (LV) and the nonlinear cross-anisotropic properties of granular base on critical pavement responses. An accurate finite element (FE) model of the pavement structure is constructed using ABAQUS software after verification. The FE model is applied for quantitative research by changing the nonlinear cross-anisotropic characteristic parameters under different LVs, which is done to determine the relationship between the critical strain responses and LVs under nonlinear cross-anisotropic properties. T

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4

Bakushev, S. V. "Flat geometric-nonlinear shear strains." Structural Mechanics of Engineering Constructions and Buildings 14, no. 6 (2018): 516–22. http://dx.doi.org/10.22363/1815-5235-2018-14-6-516-522.

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5

Nielsen, Anders S., and Ryszard Pyrz. "In-Situ Observation of Thermal Residual Strains in Carbon/Thermoplastic Microcomposites Using Raman Spectroscopy." Engineering Plastics 5, no. 4 (1997): 147823919700500. http://dx.doi.org/10.1177/147823919700500401.

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Thermal residual strains in carbon/thermoplastic microcomposites have been measured in-situ using micro Raman spectroscopy. This experimental method provides quantitative information of the relation between the level of residual strains and the temperature history. Two different microcomposites have been investigated; carbon fibre/ polycarbonate and carbon fibre/polypropylene. The observed strain-temperature profile exhibits two characteristic nonlinear zones for both composite systems. It is shown that the linear thermoelastic solution strongly overestimates residual thermal strains. In order

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6

Nielsen, Anders S., and Ryszard Pyrz. "In-Situ Observation of Thermal Residual Strains in Carbon/Thermoplastic Microcomposites Using Raman Spectroscopy." Polymers and Polymer Composites 5, no. 4 (1997): 245–56. http://dx.doi.org/10.1177/096739119700500401.

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Thermal residual strains in carbon/thermoplastic microcomposites have been measured in-situ using micro Raman spectroscopy. This experimental method provides quantitative information of the relation between the level of residual strains and the temperature history. Two different microcomposites have been investigated; carbon fibre/ polycarbonate and carbon fibre/polypropylene. The observed strain-temperature profile exhibits two characteristic nonlinear zones for both composite systems. It is shown that the linear thermoelastic solution strongly overestimates residual thermal strains. In order

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7

Simmonds, J. G. "The Strain-Energy Density of Rubber-Like Shells of Revolution Undergoing Torsionless, Axisymmetric Deformation (Axishells)." Journal of Applied Mechanics 53, no. 3 (1986): 593–96. http://dx.doi.org/10.1115/1.3171816.

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We consider a shell of revolution made of an incompressible elastically isotropic material. Assuming a torsionless, axisymmetric three-dimensional displacement field that permits large normal strains (i.e., large thickness changes) but small transverse shearing strains, we construct a two-dimensional strain-energy density for a first-approximation shell theory in which the extensional strains may be O(1). The bending strains, however, are small, as in Reissner’s nonlinear theory. An error estimate is given that depends on the undeformed thickness and curvatures, the bending strains, the transv

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8

Levin, V. A., and K. M. Zingermann. "Effective Constitutive Equations for Porous Elastic Materials at Finite Strains and Superimposed Finite Strains." Journal of Applied Mechanics 70, no. 6 (2003): 809–16. http://dx.doi.org/10.1115/1.1630811.

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A method is developed for derivation of effective constitutive equations for porous nonlinear-elastic materials undergoing finite strains. It is shown that the effective constitutive equations that are derived using the proposed approach do not change if a rigid motion is superimposed on the deformation. An approach is proposed for the computation of effective characteristics for nonlinear-elastic materials in which pores are originated after a preliminary loading. This approach is based on the theory of superimposed finite deformations. The results of computations are presented for plane stra

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9

Sokolova, M. Yu, and D. V. Khristich. "FINITE STRAINS OF NONLINEAR ELASTIC ANISOTROPIC MATERIALS." Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, no. 70 (2021): 103–16. http://dx.doi.org/10.17223/19988621/70/9.

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Anisotropic materials with the symmetry of elastic properties inherent in crystals of cubic syngony are considered. Cubic materials are close to isotropic ones by their mechanical properties. For a cubic material, the elasticity tensor written in an arbitrary (laboratory) coordinate system, in the general case, has 21 non-zero components that are not independent. An experimental method is proposed for determining such a coordinate system, called canonical, in which a tensor of elastic properties includes only three nonzero independent constants. The nonlinear model of the mechanical behavior o

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10

Johnson, A. R., T. Chen, and J. L. Mead. "Modeling Step—Strain Relaxation and Cyclic Deformations of Elastomers." Rubber Chemistry and Technology 75, no. 2 (2002): 333–45. http://dx.doi.org/10.5254/1.3544982.

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Abstract Data for step—strain relaxation and cyclic compressive deformations of highly viscous short elastomer cylinders are modeled using a large strain rubber viscoelastic constitutive theory with a rate—independent friction stress term added. In the tests, both small and large amplitude cyclic compressive strains, in the range of 1% to 10%, were superimposed on steady state compressed strains, in the range of 5% to 20%, for frequencies of 1 and 10 Hz. The elastomer cylinders were conditioned prior to each test to soften them. The constants in the viscoelastic—friction constitutive theory ar

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11

Gipple, K. L., and D. Hoyns. "Measurement of the Out-of-Plane Shear Response of Thick Section Composite Materials Using the V-Notched Beam Specimen." Journal of Composite Materials 28, no. 6 (1994): 543–72. http://dx.doi.org/10.1177/002199839402800604.

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The out-of-plane shear response of thick, unidirectional and crossply, AS4/3501-6 and S2 glass/3501-6 laminates was investigated theoretically and experimentally using V-notched beam (Iosipescu) specimens. Strains were monitored in the specimen test sections using conventional strain gages, moiré interferometry and full section strain gages. Crossply laminates exhibited a fairly uniform strain distribution away from the notches, while the unidirectional specimens were characterized by a nonuniform distribution. Measured strains correlated very well with predicted strains from specimen finite e

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12

Lee, Yung-Li, Yung J. Chiang, and Hang-Hong Wong. "A Constitutive Model for Estimating Multiaxial Notch Strains." Journal of Engineering Materials and Technology 117, no. 1 (1995): 33–40. http://dx.doi.org/10.1115/1.2804369.

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True stress and strain components at a notch are the essential parameters for fatigue life predictions. Nonlinear finite element analysis (FEA) could be the perfect solution to the notch stress and strain calculation, but its usage may be very limited due to intensive CPU time consumption. Estimation techniques for the multiaxial notch stresses and strains from linear FEA results are important and needed. The existing approach—the Hoffmann and Seeger theory—is limited for monotonic loading cases. It appears difficult to extend its application to nonproportional and variable amplitude loading c

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13

Fondrk, M. T., E. H. Bahniuk, and D. T. Davy. "Inelastic Strain Accumulation in Cortical Bone During Rapid Transient Tensile Loading." Journal of Biomechanical Engineering 121, no. 6 (1999): 616–21. http://dx.doi.org/10.1115/1.2800862.

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An experimental study examined the tensile stress-strain behavior of cortical bone during rapid load cycles to high strain amplitudes. Machined bovine and human cortical bone samples were subjected to loading cycles at a nominal load/unload rate of ±420 MPa/s. Loads were reversed at pre-selected strain levels such that load cycles were typically completed in 0.5-0.7 seconds. Axial strain behavior demonstrated considerable nonlinearity in the first load cycle, while transverse strain behavior was essentially linear. For the human bone 29.1 percent (S.D. = 4.7 percent), and for the bovine bone 3

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14

Gulzar, Saqib, and B. Shane Underwood. "Nonlinear Viscoelastic Response of Crumb Rubber Modified Asphalt Binder Under Large Strains." Transportation Research Record: Journal of the Transportation Research Board 2674, no. 3 (2020): 139–49. http://dx.doi.org/10.1177/0361198120907097.

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Agencies have been increasing their use of polymer modified asphalt binders in recent years to address performance issues and lengthen the useful life of their pavements. When deployed these materials likely experience strain levels exceeding their linear viscoelastic (LVE) limits. The same situation exists in non-polymer modified asphalt binders as well, but the effect may be more pronounced in polymer modified systems because of their bi-phasic nature. In this study, terminally blended crumb rubber (CR-TB) modified asphalt is studied to understand and quantify the nonlinear viscoelastic resp

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15

Fafitis, A., and Y. H. Won. "A Stochastic Nonlinear Constitutive Law for Concrete." Journal of Engineering Materials and Technology 111, no. 4 (1989): 443–49. http://dx.doi.org/10.1115/1.3226494.

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An incremental three-dimensional stress-strain relationship for concrete with induced anisotropy has been developed. The nonlinearity and path-dependency are modeled by expressing the elastic moduli at each increment as function of the octahedral and deviatoric strains, based on a uniaxial stochastic model developed earlier. Predictions of multiaxial response under proportional and nonproportional loading are in good agreement with experimental results.

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16

Boriek, Aladin M., Neil G. Kelly, Joseph R. Rodarte, and Theodore A. Wilson. "Biaxial constitutive relations for the passive canine diaphragm." Journal of Applied Physiology 89, no. 6 (2000): 2187–90. http://dx.doi.org/10.1152/jappl.2000.89.6.2187.

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Samples of the muscular sheet excised from the midcostal region of dog diaphragms were subjected to biaxial loading. That is, stresses in the direction of the muscle fibers and in the direction perpendicular to the fibers in the plane of the sheet were measured at different combinations of strains in the two directions. Stress-strain relations were obtained by fitting equations to these data. In the direction of the muscle fibers, for strains up to 0.7, stress is a modestly nonlinear function of strain and ranges up to ∼60 g/cm. In the direction perpendicular to the fibers, the sheet is stiffe

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17

Williams, J. L., J. H. Chen, and D. M. Belloli. "Strain Fields on Cell Stressing Devices Employing Clamped Circular Elastic Diaphragms as Substrates." Journal of Biomechanical Engineering 114, no. 3 (1992): 377–84. http://dx.doi.org/10.1115/1.2891398.

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Solutions are presented for the surface strain fields on inflated elastomeric circular diaphragms used for in vitro cell stressing experiments. It is shown, by using the method developed by Way (1934) to solve the nonlinear von Karman plate equations, that the surface strains due to bending are not negligible and that large negative radial strains arise near the clamped edge for center deflection-to-thickness ratios (w/h)< 10. The method of Hart-Smith and Crisp (1967) was used for w/h>10 to solve the nonlinear equations for symmetrical deformation of axially symmetrical rubber-like membr

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18

Golub, V. P. "Towards the solution of creep problems of thin-shelled tubular elements in isotropic nonlinear viscoelastic materials." Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, no. 1 (2019): 42–45. http://dx.doi.org/10.17721/1812-5409.2019/1.8.

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A new approach to the creep strains analysis of thin-shelled tubular elements in isotropic nonlinear viscoelastic materials under combined loading with uniaxial tension and torsion has been proposed. The system of equations that is constructed according to the deviators proportionality hypothesis has been chosen as the creep constitutive equations the nonlinearity of viscoelastic properties in which is given with respect to the creep strain intensity and volumetric strain by the Rabotnov type models. The kernels of creep strain intensity and volumetric strain are given by the relations that es

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19

Suhir, E. "Effect of the Nonlinear Behavior of the Material on Two-Point Bending of Optical Glass Fibers." Journal of Electronic Packaging 114, no. 2 (1992): 246–50. http://dx.doi.org/10.1115/1.2906425.

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We evaluate the effect of the nonlinear stress-strain relationship on the maximum curvature and maximum stress in optical glass fibers subjected to two-point bending. The analysis uses an assumption that this relationship, obtained experimentally for the case of uniaxial tension (Mallinder and Proctor, 1964; Kraus, Testardi, and Thurston, 1979, Glaesemann, Gulati, and Helfinstine, 1988), holds in the case of compression as well, and is applicable also to bending deformations. We show that the shift in the neutral axis due to the nonlinear stress-strain relationship has a significant effect on

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20

Norris, A. N., and D. L. Johnson. "Nonlinear Elasticity of Granular Media." Journal of Applied Mechanics 64, no. 1 (1997): 39–49. http://dx.doi.org/10.1115/1.2787292.

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The finite and incremental elasticity of a random packing of identical spheres is derived using energy methods. We consider different models for the contact forces between spheres, all of which are based upon or related to the fundamental Hertz theory; we consider only the special cases of perfect friction (no tangential slip) or no tangential friction. The existence of a strain energy function for the medium depends critically upon the type of contact. If the tangential contact stiffness is independent of the normal force, then the energy is well defined for all values of the macroscopic stra

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21

Liu, Gang, Suxia Xia, Bin Hou, Tao Gao, and Ru Zhang. "Mechanical stabilities and nonlinear properties of monolayer Gallium selenide under tension." Modern Physics Letters B 29, no. 12 (2015): 1550049. http://dx.doi.org/10.1142/s0217984915500499.

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The mechanical stabilities and nonlinear properties of monolayer Gallium selenide ( GaSe ) under tension are investigated by using density functional theory (DFT). The ultimate stresses and ultimate strains and the structure evolutions of monolayer GaSe under armchair (AC), zigzag (ZZ) and equiaxial (EQ) tensions are predicted. A thermodynamically rigorous continuum description of nonlinear elastic response is given by expanding the elastic strain energy density in a Taylor series in Lagrangian strain truncated after the fifth-order term. Fourteen nonzero independent elastic constants are dete

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22

Adolfsson, Klas. "Nonlinear Fractional Order Viscoelasticity at Large Strains." Nonlinear Dynamics 38, no. 1-4 (2004): 233–46. http://dx.doi.org/10.1007/s11071-004-3758-4.

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23

Sokolova, Marina, Vadim Rudakov, and Dmitrii Khristich. "Strains of plates of nonlinear anisotropic materials." Journal of Physics: Conference Series 1203 (April 2019): 012024. http://dx.doi.org/10.1088/1742-6596/1203/1/012024.

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24

Creswell, L. L., M. J. Moulton, S. G. Wyers, et al. "An experimental method for evaluating constitutive models of myocardium in in vivo hearts." American Journal of Physiology-Heart and Circulatory Physiology 267, no. 2 (1994): H853—H863. http://dx.doi.org/10.1152/ajpheart.1994.267.2.h853.

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A new experimental method for the evaluation of myocardial constitutive models combines magnetic resonance (MR) radiofrequency (RF) tissue-tagging techniques with iterative two-dimensional (2-D) nonlinear finite element (FE) analysis. For demonstration, a nonlinear isotropic constitutive model for passive diastolic expansion in the in vivo canine heart is evaluated. A 2-D early diastolic FE mesh was constructed with loading parameters for the ventricular chambers taken from mean early diastolic-to-late diastolic pressure changes measured during MR imaging. FE solution was performed for regiona

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25

Johnson, P. A., and P. N. J. Rasolofosaon. "Manifestation of nonlinear elasticity in rock: convincing evidence over large frequency and strain intervals from laboratory studies." Nonlinear Processes in Geophysics 3, no. 2 (1996): 77–88. http://dx.doi.org/10.5194/npg-3-77-1996.

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Abstract. Nonlinear elastic response in rock is established as a robust and representative characteristic rock rather than a curiosity. We show measurements of this behaviour from a variety of experiments on rock taken over many orders of magnitude in strain and frequency. The evidence leads to a pattern of unifying behaviour in rock: (1) Nonlinear response in rock is ubiquitous. (2) The response takes place over a large frequency interval (dc to 105 kHz at least). (3) The response not only occurs, as is commonly appreciated, large strains but also at small strains where this behaviour and the

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26

Hokstad, Ketil. "Nonlinear and dispersive acoustic wave propagation." GEOPHYSICS 69, no. 3 (2004): 840–48. http://dx.doi.org/10.1190/1.1759470.

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Because of cracks and poor consolidation, rocks may have large third‐and fourth‐order nonlinear elastic moduli. Even though strains are small, nonlinear effects may be important in acoustic wave transmission experiments. A nonlinear and dispersive extension of Hooke's law is proposed. Combined with Newton's law, this gives a nonlinear and dispersive acoustic wave equation. For some combinations of nonlinear and dispersive parameters, the wave equation can be reduced to the Korteweg‐deVries equation, such that analytical solutions can be obtained. Finite‐difference simulations with an initial R

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27

Shin, Jong Gye, and Cheol Ho Ryu. "Nonlinear Kinematic Analysis of the Deformation of Plates for Ship Hull Fabrication." Journal of Ship Research 44, no. 04 (2000): 270–77. http://dx.doi.org/10.5957/jsr.2000.44.4.270.

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Curved plates in a ship's hull are fabricated by mechanical or thermal processes, such as roller bending and line heating methods. The formation of curved plates is a process in which, from the point of view of mechanics, permanent bending and/or in-plane strains are applied to flat plates. Only bending strains are applied to single curvature shells, while in-plane strains, in addition to bending strains, need to be applied in order to form double curvature shells. In-plane strains, however, are known to be small and, thus, can be neglected. The mechanics of plate bending is different from the

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28

Schmidt, Ruediger, and Thang Duy Vu. "Nonlinear Dynamic FE Simulation of Smart Piezolaminated Structures Based on First- and Third-Order Transverse Shear Deformation Theory." Advanced Materials Research 79-82 (August 2009): 1313–16. http://dx.doi.org/10.4028/www.scientific.net/amr.79-82.1313.

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This paper deals with nonlinear finite element analysis of smart structures with integrated piezoelectric layers. Two geometrically nonlinear finite plate elements incorporating piezoelectric layers are applied based either on first- or third-order transverse shear deformation theory. Nonlinear strain-displacement relations are used that are valid for small strains and moderate rotations. Numerical tests are performed for the time histories of the tip displacement and sensor output voltage of a thin beam with a piezoelectric patch bonded to the surface.

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29

Finney, Robert H., and Alok Kumar. "Development of Material Constants for Nonlinear Finite-Element Analysis." Rubber Chemistry and Technology 61, no. 5 (1988): 879–91. http://dx.doi.org/10.5254/1.3536224.

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Abstract The determination of the material coefficients for Ogden, Mooney-Rivlin, Peng, and Peng-Landel material models using simple ASTM D 412 tensile data is shown to be a manageable task. The application of the various material models are shown to be subject to the type and level of deformation expected, with Ogden showing the best correlation with experimental data over a large strain range for the three types of strain investigated. At low strains, all of the models showed reasonable correlation.

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Gülümser, Emir, Uğur Güdükbay, and Sinan Filiz. "Fast Stiffness Matrix Calculation for Nonlinear Finite Element Method." Journal of Applied Mathematics 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/932314.

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We propose a fast stiffness matrix calculation technique for nonlinear finite element method (FEM). Nonlinear stiffness matrices are constructed using Green-Lagrange strains, which are derived from infinitesimal strains by adding the nonlinear terms discarded from small deformations. We implemented a linear and a nonlinear finite element method with the same material properties to examine the differences between them. We verified our nonlinear formulation with different applications and achieved considerable speedups in solving the system of equations using our nonlinear FEM compared to a stat

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31

Ng, Charles WW, B. Simpson, M. L. Lings, and DFT Nash. "Numerical analysis of a multipropped excavation in stiff clay." Canadian Geotechnical Journal 35, no. 1 (1998): 115–30. http://dx.doi.org/10.1139/t97-074.

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This paper presents the procedures and the results of numerical analyses of a multipropped deep excavation at Lion Yard, Cambridge, using the nonlinear Brick model. The computed results are compared with the comprehensive case record. The observed small deflections and bending moments of the wall, low prop forces, and relatively small ground movements during the main excavation have been taken into account. Shear strains which developed around the site during the main excavation were generally less than 0.3%. Significant reduction of lateral stress in the ground during wall installation and th

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Coulais, Corentin. "Periodic cellular materials with nonlinear elastic homogenized stress-strain response at small strains." International Journal of Solids and Structures 97-98 (October 2016): 226–38. http://dx.doi.org/10.1016/j.ijsolstr.2016.07.025.

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Ye, Yong, and Yi Zhou Cai. "The Nonlinear Viscoelastic Behavior for Asphalt Mixture Materials." Advanced Materials Research 255-260 (May 2011): 3268–71. http://dx.doi.org/10.4028/www.scientific.net/amr.255-260.3268.

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Compressive behavior of asphalt mixture is studied in creep and strain recovery tests observing large nonlinear viscoelastic strains. The nonlinear viscoelastic material model for asphalt mixture is presented, based on a modified version of Schapery’s constitutive relationship. For the description of the nonlinear viscoelastic response of the material, simple creep and recovery tests for different stress levels were executed. An analytical method and a nonlinear fitting procedure by the least square method are developed to determine nonlinear viscoelastic stress dependent parameters. Constant

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Wyatt, Hayley, Alexander Safar, Alastair Clarke, Sam L. Evans, and L. Angela Mihai. "Nonlinear scaling effects in the stiffness of soft cellular structures." Royal Society Open Science 6, no. 1 (2019): 181361. http://dx.doi.org/10.1098/rsos.181361.

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For cellular structures with uniform geometry, cell size and distribution, made from a neo-Hookean material, we demonstrate experimentally that large stretching causes nonlinear scaling effects governed by the microstructural architecture and the large strains at the cell level, which are not predicted by the linear elastic theory. For this purpose, three honeycomb-like structures with uniform square cells in stacked distribution were designed, where the number of cells varied, while the material volume and the ratio between the thickness and the length of the cell walls were fixed. These stru

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Xie, Jiaping, Jianbo Zhou, and Y. C. Fung. "Bending of Blood Vessel Wall: Stress-Strain Laws of the Intima-Media and Adventitial Layers." Journal of Biomechanical Engineering 117, no. 1 (1995): 136–45. http://dx.doi.org/10.1115/1.2792261.

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In order to determine the stress-strain relationship of the inner (intima and media) and outer (adventitia) layers of blood vessels in the neighborhood of the zero-stress state, bending experiments were performed on aortic strips of rats. In the experiments, one end of a strip was clamped, and a force was applied on the other end. The deflection curves of the strips were measured. By regarding the aortic strip as a curved beam, the classical beam theory was employed to analyze the strain distribution from the experimental data. A computer program dealing with nonlinear equations and nonlinear

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Bauchau, O. A., and C. H. Hong. "Nonlinear Composite Beam Theory." Journal of Applied Mechanics 55, no. 1 (1988): 156–63. http://dx.doi.org/10.1115/1.3173622.

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The modeling of naturally curved and twisted beams undergoing arbitrarily large displacements and rotations, but small strains, is a common problem in numerous engineering applications. This paper has three goals: (1) present a new formulation of this problem which includes transverse shearing deformations, torsional warping effects, and elastic couplings resulting from the use of composite materials, (2) show that the small strain assumption must be applied in a consistent fashion for composite beams, and (3) present some numerical results based on this new formulation to assess its accuracy,

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Kolpakov, A. G., and S. I. Rakin. "Deformation Characteristics of Laminar Composites under Nonlinear Strains." Journal of Applied Mechanics and Technical Physics 45, no. 5 (2004): 747–55. http://dx.doi.org/10.1023/b:jamt.0000037974.11826.75.

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Achour, B., and T. M. Roberts. "Nonlinear strains and instability of thin-walled bars." Journal of Constructional Steel Research 56, no. 3 (2000): 237–52. http://dx.doi.org/10.1016/s0143-974x(99)00072-3.

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Simon, S. I., and G. W. Schmid-Scho¨nbein. "Kinematics of Cytoplasmic Deformation in Neutrophils During Active Motion." Journal of Biomechanical Engineering 112, no. 3 (1990): 303–10. http://dx.doi.org/10.1115/1.2891188.

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A procedure is proposed to measure the cytoplasmic deformation in active motile neutrophils in the form of cytoplasmic strains and strain rates. Three neighboring microspheres in a local region of the cytoplasm serve as markers for local motion. Their positions are tracked by means of a high resolution light microscope and serve to compute nonlinear measures of strains and strain rates together with the principal strains and principal directions. Active neutrophils exhibit large cytoplasmic strains both during periodic pseudopod projections and during continuous locomotion in a polarized shape

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Zhai, Zhanyu, Bingyan Jiang, and Dietmar Drummer. "Nonlinear Material Model for Quasi-Unidirectional Woven Composite Accounting for Viscoelastic, Viscous Deformation, and Stiffness Reduction." Polymers 10, no. 8 (2018): 903. http://dx.doi.org/10.3390/polym10080903.

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To clarify the individual contribution of viscoelastic and viscous deformation to the global nonlinear response of composites, multilevel cyclic loading-unloading recovery tensile tests were carried out. The experimental results show that there is a linear relationship between the viscous strain and viscoelastic strain of composites, regardless of the off-axis angle or loading stress level. On the basis of experimental results, a coupled damage-plasticity constitutive model was proposed. In this model, the plasticity theory was adopted to assess the evolution of viscous strains. The viscoelast

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Montero Guarda, Sebastian, Roger Bustamante Plaza, and Alejandro Ortiz Bernardin. "On the behaviour of spherical inclusions in a cylinder under tension loads." Ingenius, no. 19 (January 1, 2018): 69–78. http://dx.doi.org/10.17163/ings.n19.2018.07.

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In the present paper the behaviour of a hyperelastic body is studied, considering the presence of one, two and more spherical inclusions, under the effect of an external tension load. The inclusions are modeled as nonlinear elastic bodies that undergo small strains. For the material constitutive relation, a relatively new type of model is used, wherein the strains (linearized strain) are assumed to be nonlinear functions of the stresses. In particular, it is used a function such that the strains are always small, independently of the magnitude of the external loads. In order to simplify the pr

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Nazzal, Mohammad, and Marwan K. Khraisheh. "On The Stability of Superplastic Deformation Using Nonlinear Wavelength Analysis." Key Engineering Materials 344 (July 2007): 47–54. http://dx.doi.org/10.4028/www.scientific.net/kem.344.47.

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Optimum variable strain rate forming paths based on two multiscale deformation-based stability criteria are developed. The first criterion is based on Hart’s linear stability analysis while in the second criterion; we introduce a modified one dimensional nonlinear long wavelength analysis introduced by Hutchinson and Neale [7] based on the well known 2-D Marciniak-Kuczynski criterion. The stability criteria are calibrated for the AZ31 Mg alloy at 400 °C yielding two different variable strain rate forming paths. These paths show that the nonlinear wavelength analysis is more sensitive to strain

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Fahrenthold, E. P., and K. E. Gray. "A Nonlinear Compaction Model for Sandstone." Journal of Energy Resources Technology 108, no. 2 (1986): 146–55. http://dx.doi.org/10.1115/1.3231254.

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Constitutive relations for the compaction behavior of porous sandstone have been formulated to describe the results of uniaxial and triaxial tests under reservoir pressure and temperature conditions. An expression for loading behavior in uniaxial compression is derived by treating the loading modulus as an independent variable. Similar relations are derived for uniaxial and triaxial compaction tests. Elastic unloading takes a quadratic form when described by incremental stresses and strains. The constitutive equations relate the values of the incremental stress and strain on loading and unload

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Warren, W. E., and A. M. Kraynik. "The Nonlinear Elastic Behavior of Open-Cell Foams." Journal of Applied Mechanics 58, no. 2 (1991): 376–81. http://dx.doi.org/10.1115/1.2897196.

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A constitutive model for the nonlinear elastic behavior of isotropic low-density opencell foams with three-dimensional structure is formulated in terms of a strain energy function. The theory is based on micromechanical analysis of an idealized tetrahedral unit cell of arbitrary orientation that contains four half-struts joining at equal angles. The force-displacement relations for each strut are expressed by compliances for bending and stretching that do not depend on the magnitude of applied force. Contributions to the strain energy from large deformation effects are assumed to depend on str

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That-Hoang, Lan T., Hieu Nguyen-Van, Thanh Chau-Dinh, and Chau Huynh-Van. "Enhancement to four-node quadrilateral plate elements by using cell-based smoothed strains and higher-order shear deformation theory for nonlinear analysis of composite structures." Journal of Sandwich Structures & Materials 22, no. 7 (2018): 2302–29. http://dx.doi.org/10.1177/1099636218797982.

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This paper improves four-node quadrilateral plate elements by using cell-based strain smoothing enhancement and higher-order shear deformation theory (HSDT) for geometrically nonlinear analysis of composite structures. Small strain-large displacement theory of von Kármán is used in nonlinear formulations of four-node quadrilateral plate elements that have strain components smoothed or averaged over the sub-domains of the elements. From the divergence theory, the displacement gradients in the smoothed strains are transformed from the area integral into the line one. The behavior of composite st

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Taber, L. A. "On a Nonlinear Theory for Muscle Shells: Part I—Theoretical Development." Journal of Biomechanical Engineering 113, no. 1 (1991): 56–62. http://dx.doi.org/10.1115/1.2894085.

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This paper presents a theory for studies of the large-strain behavior of biological shells composed of layers of incompressible, orthotropic tissue, possibly muscle, of arbitrary orientation. The intrinsic equations of the laminated-shell theory, expressed in lines-of-curvature coordinates, account for large membrane [O(1)] and moderately large bending and transverse shear strains [O(0.3)], nonlinear material properties, and transverse normal stress and strain. An expansion is derived for a general two-dimensional strain-energy density function, which includes residual stress and muscle activa

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Elad, D., A. Foux, and Y. Kivity. "A Model for the Nonlinear Elastic Response of Large Arteries." Journal of Biomechanical Engineering 110, no. 3 (1988): 185–89. http://dx.doi.org/10.1115/1.3108429.

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The nonlinear elastic response of large arteries subjected to finite deformations due to action of biaxial principal stresses, is described by simple constitutive equations. Generalized measures of strain and stress are introduced to account for material nonlinearity. This also ensures the existence of a strain energy density function. The orthotropic elastic response is described via quasi-linear relations between strains and stresses. One nonlinear parameter which defines the measures of strain and stress, and three elastic moduli are assumed to be constants. The lateral strain parameters (e

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Xu, Fangyuan, Yuanli Chen, Xianglong Zheng, Rujin Ma, and Hao Tian. "Experimental Study on Corrosion and Mechanical Behavior of Main Cable Wires Considering the Effect of Strain." Materials 12, no. 5 (2019): 753. http://dx.doi.org/10.3390/ma12050753.

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To study the corrosion degradation of cable wires in a bridge’s life, this research work created an accelerated corrosion test device, which sought to identify an optimal constant strain level. An accelerated corrosion test was carried out and the corroded specimens were scanned using super depth 3D microscopy technology. Mass loss and minimum cross-sectional diameter was measured to understand the degradation characteristics of cable wires at variable strains and corrosion time. The variation of elastic modulus, yield load, and ultimate load of corroded wires, subjected to a tensile test, wer

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Orgill, G., and J. F. Wilson. "Finite Deformations of Nonlinear, Orthotropic Cylindrical Shells." Journal of Applied Mechanics 53, no. 2 (1986): 257–65. http://dx.doi.org/10.1115/1.3171749.

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The nonbuckling finite deformations of an orthotropic, thin wall cylinder are investigated. The cylinder is made of a nonlinear material and subjected to internal pressure, end load and torque. Initially the stresses and strains in the cylinder are assumed to be axially homogeneous. The model is then extended to include axially nonhomogeneous stresses and strains that may arise due to particular displacement boundary conditions such as radial confinement at the edges. The loads are applied to the cylinder incrementally, the finite strains are computed, and adjustments are made in cylinder dime

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Levin, Vladimir A., Anatoly V. Vershinin, and Konstantin M. Zingerman. "Numerical Analysis of Propagation of Nonlinear Waves in Prestressed Solids." Modern Applied Science 10, no. 4 (2016): 158. http://dx.doi.org/10.5539/mas.v10n4p158.

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<p>The details of numerical algorithms implemented in CAE FIDESYS for the analysis of the propagation of nonlinear waves in elastic and viscoelastic bodies are discussed. It’s taken into account that waves propagation lead to new strains which superimpose on existing stresses (induced anisotropy) in the media. For the formulation of problem we used the theory of repeated superposition of large strains. The details of numerical algorithms for the analysis of the propagation of nonlinear waves in elastic and viscoelastic bodies are discussed. The implementation of the spectral element meth

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