Статті в журналах: "NONLINEAR STRAINS"

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 (February 16, 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 AA6061 aluminum alloy tube under a set of linear loading paths and two typical nonlinear loading paths were tested. Parameter values of the M-K+DF2012 model for the tube were determined based on the experimental limit strains under linear loading paths, and the limit strains under the two nonlinear loading paths were predicted. Then the strain-based forming limit diagram (ε-FLD) and the polar effective plastic strain FLD (PEPS-FLD) of the tube under different pre-strains were predicted and discussed. The results show that the limit strains of the tube are obviously path-dependent, and the M-K+DF2012 model can reasonably capture the limit strains of the tube under both linear and nonlinear loading paths. The predicted ε-FLD shows a strong dependence on the pre-strain, while the predicted PEPS-FLD is weakly strain path-dependent and almost path-independent on the right-hand side for the AA6061 tube.

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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 (October 16, 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 compression. The nonlinearity was quantified by the reduction in tangent modulus at 0.20 percent and 0.40 percent strain as compared to the initial modulus. For the pooled data, the mean±SD percentage reduction in tangent modulus at 0.20 percent strain was 9.07±3.24 percent in compression and 13.8±4.79 percent in tension. At 0.40 percent strain, these values were 23.5±5.71 and 35.7±7.10 percent, respectively. The magnitude of the nonlinearity depended on both anatomic site p<0.001 and loading mode p<0.001, and in tension was positively correlated with density. Calculated values of elastic modulus and yield properties depended on the strain range chosen to define modulus via a linear curve fit p<0.005. Mean percent differences in 0.20 percent offset yield strains were as large as 10.65 percent for some human sites. These results establish that trabecular bone exhibits nonlinearity at low strains, and that this behavior can confound intersite comparisons of mechanical properties. A nonlinear characterization of the small strain behavior of trabecular bone was introduced to characterize the initial stress–strain behavior more thoroughly.

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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 (January 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. The transverse tensile strain is found to be exerted on the pavement for a longer amount of time than the longitudinal tensile strain. It also found that the critical longitudinal, transverse, and shear strains can be described as having exponential relationships. The exponent coefficients indicate that the influences of the LV on these three types of strains are analogical. In other words, with the increase of tire velocity, the critical strains decay exponentially. The LV is found to have a limited impact on the compressive strain under the same nonlinear cross-anisotropic properties. However, the effects of nonlinear cross-anisotropic properties on the compressive strain at the top of the subgrade are obvious.

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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 (January 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 to overcome this deficiency the thermorheologically simple model is applied to predict residual strains. The results indicate that the model correctly estimates the level of residual strains in thermoplastic microcomposites, but fails to describe the two nonlinear characteristic zones. This leads to the conclusion that a more complex constitutive model of the matrix phase must be considered.

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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 (January 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 to overcome this deficiency the thermorheologically simple model is applied to predict residual strains. The results indicate that the model correctly estimates the level of residual strains in thermoplastic microcomposites, but fails to describe the two nonlinear characteristic zones. This leads to the conclusion that a more complex constitutive model of the matrix phase must be considered.

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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 (September 1, 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 transverse shearing strain, and the characteristic wavelength of the shell theory solutions.

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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 (November 1, 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 strain, when pores are distributed uniformly.

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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 of cubic materials is developed, taking into account geometric and physical nonlinearities. The specific potential strain energy for a hyperelastic cubic material is written as a function of the tensor invariants, which are projections of the Cauchy-Green strain tensor into eigensubspaces of the cubic material. Expansions of elasticity tensors of the fourth and sixth ranks in tensor bases in eigensubspaces are determined for the cubic material. Relations between stresses and finite strains containing the second degree of deformations are obtained. The expressions for the stress tensor reflect the mutual influence of the processes occurring in various eigensubspaces of the material under consideration.

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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 (May 1, 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 are determined by employing a nonlinear least-squares method to fit the analytical stresses for a Maxwell model, which includes friction, to measured relaxation stresses obtained from a 20% step—strain compression test. The simulation of the relaxation data with the nonlinear model is successful at compressive strains of 5%, 10%, 15%, and 20%. Simulations of hysteresis stresses for enforced cyclic compressive strains of 20%±5% are made with the model calibrated by the relaxation data. The predicted hysteresis stresses are lower than the measured stresses.

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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 (April 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 element analyses using nonlinear elastic material properties.

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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 (January 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 cases. A generalized method for estimating multiaxial notch stresses and strains on the basis of elastic stress solutions is presented here. This method utilizes a two-surface model with the Mroz hardening equation and the associated flow rule to simulate the local notch stress and strain responses for any geometrical constraints of specimens under monotonic, in-phase and out-of-phase loading. The uniaxial material properties associated with the two-surface model are determined by: the Neuber rule, the Glinka rule and FEA results. Comparisons are made with the notch strains calculated by nonlinear FEA and those obtained from strain gages. Reasonable correlations between the measured and predicted notch strains are observed for SAE 1045 material.

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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 (December 1, 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 35.1 percent (S.D. = 10.8 percent) of the maximum nonlinear strain accumulated after load reversal, where nonlinear strain was defined as the difference between total strain and strain corresponding to linear elastic behavior. Average residual axial strain on unloading was 35.4 percent (S.D. = 1.2 percent) for human bone and 35.1 percent (S.D. = 2.9 percent) of maximum nonlinear strain. Corresponding significant volumetric strains and residual volumetric strains were found. The results support the conclusions that the nonlinear stress-strain behavior observed during creep loading also occurs during transient loading at physiological rates. The volume increases suggest that damage accumulation, i.e., new internal surfaces and voids, plays a major role in this behavior. The residual volume increases and associated disruptions in the internal structure of bone provide a potential stimulus for a biological repair response.

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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 (February 27, 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 response under large strains. The CR-TB binders are extensively used in pavements subjected to high vehicular loads and extreme climatic conditions; thereby, their response under large strains becomes more critical. The current standard characterization techniques are based on LVE response using small amplitude oscillatory shear rheology only and do not consider the behavior of binders under large strains. In this study, large amplitude oscillatory shear (LAOS) rheology is used as a framework to more thoroughly investigate the complete response of the CR-TB modified asphalt binder under large strains at 30°C, 40°C, 50°C, and 60°C and at the frequencies of 0.5, 1, and 5 Hz. The LAOS response is analyzed using Fourier-transform rheology and the orthogonal stress decomposition method involving Chebyshev polynomial representation. It is found that nonlinearity manifests greatly in this study material as strain levels increase and frequencies decrease. The relative nonlinearity increases with increasing strain amplitude and is more significant towards lower end of the tested temperature range. The CR-TB binder shows strain-stiffening/softening and shear-thinning/thickening behavior depending upon a specific temperature, strain level, and frequency.

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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 (October 1, 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 (December 1, 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 stiffer and more strongly nonlinear. At a strain in the perpendicular direction of ∼0.35, stress increases abruptly. The stress-strain relation in the muscle direction is consistent with observations of passive muscle shortening in vivo. However, the stiffness in the perpendicular direction is not high enough to explain the observation that strains in the perpendicular direction in vivo are nearly zero. We conclude that, in the passive diaphragm in vivo, stress in the direction perpendicular to the muscle fibers is small.

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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 (August 1, 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 membranes. In the membrane solutions the circumferential strains drop parabolically to zero at the clamped edge of the diaphragm, while the radial strains increase slightly with the radius. The solutions for w/h>10 are compared to optical measurements of in-plane displacements used to calculate the circumferential strains on the diaphragm, yielding excellent agreement with the theory.

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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 establish the relationships between these kernels and one-dimensional creep kernels determined from a system of base experiments. One-dimensional tension with the measurement of longitudinal and transverse strains as well as one-dimensional tension and pure torsion with the measurement of longitudinal and shearing strains have been considered as base experiments. The functions of nonlinearity of viscoelastic properties are given by smoothing cubic splines. The problems of the analysis of longitudinal, transverse and shearing strains of thin-shelled tubular specimens made of “high density polyethylene PEHD” have been solved and experimentally approved.

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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 (June 1, 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 the maximum stress, while its effect on the maximum curvature is small and need not be considered. We show also that this relationship, obtained for elastic strains, not exceeding 5 percent, cannot be applied for very large strains, and therefore the future experimental work should include the evaluation of the nonlinear behavior of the material, both in tension and compression, for higher strains and for high strength fibers (such as, for instance, fibers protected by metallic coatings). The obtained results can be helpful in the analysis of optical glass fibers subjected to two-point bending.

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20

Norris, A. N., and D. L. Johnson. "Nonlinear Elasticity of Granular Media." Journal of Applied Mechanics 64, no. 1 (March 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 strain. Otherwise, the strain energy of the system is path dependent, in general. However, the concept of a quadratic strain energy function is always well defined for incremental motion superimposed on large confining stress and strain. For all models considered, we derive the changes in wave speeds due to incremental strains. For the models based upon an energy function we derive expressions for the third-order elastic constants as a function of confining pressure.

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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 (May 10, 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 determined by least-square fit to the DFT calculations. Pressure-dependent elastic constants (Cij(P)) and pressure derivatives of [Formula: see text] are also calculated. Calculated values of ultimate stresses and strains and the in-plane Young's modulus are all positive. It proves that monolayer GaSe is mechanically stable.

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22

Adolfsson, Klas. "Nonlinear Fractional Order Viscoelasticity at Large Strains." Nonlinear Dynamics 38, no. 1-4 (December 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, J. S. Pirolo, D. S. Fishman, W. H. Perman, K. W. Myers, 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 (August 1, 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 regional, intramyocardial ventricular wall strains using small-strain, small-displacement theory. Corresponding regional ventricular wall strains were computed independently using MR images that incorporated RF tissue tagging. Two unknown parameters were determined for an exponential strain energy function that maximized agreement between observed (from MR) and predicted (from FE analysis) regional wall strains. Extension of this methodology will provide a framework in which to evaluate the quality of myocardial constitutive models of arbitrary complexity on a regional basis.

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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 (June 30, 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 manifestations of this behaviour are commonly disregarded.

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26

Hokstad, Ketil. "Nonlinear and dispersive acoustic wave propagation." GEOPHYSICS 69, no. 3 (May 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 Ricker wavelet show that the nonlinear terms in the wave equation steepen the wavefront and higher harmonics in the frequency spectrum. When dispersion is included, a nonlinear stress–strain relation with hysteresis is observed.

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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 (December 1, 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 production of plate bending. In the mechanics of plate bending, an initial configuration of a plate is given, along with boundary and loading conditions. The deformed shape can then be calculated. In the production of plate bending, however, only the final deformation shape is given and the initial configuration is unknown. Loading conditions must also be determined. This paper presents rigorous formulations of a kinematic problem for the production of plate bending. Nonlinear kinematic analysis with and without initial imperfections is employed in order to include in-plane strains. An algorithm is suggested to determine an initial configuration from given surface data. Numerical examples show that the in-plane strain must not be negligible and, rather, plays an important role in the determination of heating paths in the line heating method.

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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 (November 1, 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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30

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 state-of-the-art nonlinear FEM.

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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 (February 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 the highly nonlinear stress-strain characteristics of the Gault Clay are the chief reasons for the observed unusual behaviour. The Gault Clay exhibits first yield at a threshold shear strain of about 0.001%, beyond which the stiffness deteriorates significantly from an initial very high value. This high stiffness at very small strains may be due to cementation bonding between soil particles, as a result of the presence of calcium carbonate. Simple drainage assumptions for the stiff fissured clay on both sides of the diaphragm wall appear to be inadequate for design analyses.Key words: numerical analysis, multipropped excavation, Gault Clay, nonlinear brick model, small strain stiffness.

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32

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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33

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 stress creep testing were also performed to validate the developed material model. The model successfully describes the main features for asphalt mixture and shows good agreement with test data within the considered stress range.

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34

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 (January 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 structures were manufactured from silicone rubber and tested under large uniaxial tension in a bespoke test fixture. Optical strain measurements were used to assess the deformation by capturing both the global displacements of the structure and the local deformations in the form of a strain map. The experimental results showed that, under sufficiently large strains, there was an increase in the stiffness of the structure when the same volume of material was arranged as many small cells compared to when it was organized as fewer larger cells. Finite element simulations confirmed our experimental findings. This study sheds light upon the nonlinear elastic responses of cellular structures in large-strain deformations, which cannot be captured within the linear elasticity framework.

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35

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 (February 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 least squares optimization was developed. Strains were referred to the zero-stress state. The load-deflection relationship was then used to determine the stress-strain relationship. Certain forms of the stress-strain laws were assumed. The linear laws fit the experimental data accurately, probably because the strains during bending are quite small, although the rotations are large. The Young’s modulus of the inner layer, which consists of endothelial and smooth muscle cells and elastic lamina, was found to be three to four times larger than that of the outer layer which consists of collagen with a small amount of fibroblasts and elastin. The residual stresses and strains at the no-load state were calculated from the deduced stress-strain relationship. It is shown that large errors (up to 50 percent) in the values of the residual strains will occur if the wall material was treated as homogeneous, i.e., if the layered constitution was ignored.

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36

Bauchau, O. A., and C. H. Hong. "Nonlinear Composite Beam Theory." Journal of Applied Mechanics 55, no. 1 (March 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, and to point out some distinguishing feature of anisotropic beam behavior. First, the predictions of the formulation will be compared with experimental results for the large deflections and rotations of an aluminum beam. Then, the distinguishing features of composite beams that are likely to impact the design of rotating blades (such as helicopter blades) will be discussed. A first type of extension-twisting coupling introduced by the warping behavior of a pretwisted beam is discussed, then, a shearing strain squared term, usually neglected in small strain analyses, is shown to introduce a coupling between axial extension and twisting behavior, that can be significant when the ratio E/G is large (E and G are Young’s and shearing moduli of the beam, respectively). Finally, the impact of inplane shearing modulus changes and torsional warping constraints on the behavior of beams exhibiting elastic couplings is investigated.

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37

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 (September 2004): 747–55. http://dx.doi.org/10.1023/b:jamt.0000037974.11826.75.

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38

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

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39

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 (August 1, 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. The cytoplasmic motion is often synchronized with the whole cell deformation. The local cytoplasmic strains exceed the strains estimated for the whole cell and are not reversible except in some cases of single pseudopod projections. Large strains are observed both in attached and freely suspended cells. Strain rates are relatively constant but show an increase during the pseudopod retraction phase. Local cytoplasmic strains in neutrophils are inhomogeneous and reach large values during passage of the contraction rings. Neutrophils rendered passive by treatment with cytochalasin or EDTA show a random motion of microspheres with much smaller displacements. These observations suggest that the cytoplasm of active neutrophil exhibits large cytoplasmic strains and strain rates in the absence of an external stress resulting in a high degree of intracellular mixing. The proposed technique may be applied to a wide range of problems in cell biology.

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40

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 (August 11, 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 viscoelastic strain was represented as a linear function of viscous strains. Moreover, the Weibull function of the effective stress was introduced to evaluate the damage variables in terms of stiffness reduction. The tensile stress-strain curves, predicted by the proposed model, showed a good agreement with experimental results.

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41

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 problem, the hyperelastic medium and the inclusions are modelled as axial-symmetric bodies. The finite element method is used to obtain results for these boundary value problems. The objective of using these new models for elastic bodies in the case of the inclusions is to study the behaviour of such bodies in the case of concentration of stresses, which happens near the interface with the surrounding matrix. From the results presented in this paper, it is possible to observe that despite the relatively large magnitude for the stresses, the strains for the inclusions remain small, which would be closer to the actual behaviour of real inclusions made of brittle materials, which cannot show large strains.

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42

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 rate sensitivity and results in larger attainable uniform strains than Hart’s approach especially at low strain rates. This result is demonstrated through finite element simulations of a deep rectangular box using pressure profiles derived from the two variable strain rate forming paths. The FE results clearly illustrate that Hart’s approach underestimates the amount of uniform deformation and therefore prolongs the forming time to prevent failure compared to the nonlinear analysis.

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43

Fahrenthold, E. P., and K. E. Gray. "A Nonlinear Compaction Model for Sandstone." Journal of Energy Resources Technology 108, no. 2 (June 1, 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 unloading using parameters that are a function of the state of prestress in the material. Published data on samples cored from three different wells at various depths exhibited a similar dependence of rock properties on mechanical and pore pressure loads.

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44

Warren, W. E., and A. M. Kraynik. "The Nonlinear Elastic Behavior of Open-Cell Foams." Journal of Applied Mechanics 58, no. 2 (June 1, 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 strut reorientation and stretching, and are determined by analyzing a pin-jointed structure. The analysis is considered to be valid for finite strains below the onset of yielding associated with strut buckling.

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45

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 (August 31, 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 structures follows the third-order shear deformation theory. The solution of the nonlinear equilibrium equations is obtained by the iterative method of Newton–Raphson with the appropriate convergence criteria. The present numerical results are compared with the other numerical results available in the literature in order to demonstrate the effectiveness of the developed element. These results also contribute a better knowledge and understanding of nonlinear bending behaviors of these composite structures.

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46

Taber, L. A. "On a Nonlinear Theory for Muscle Shells: Part I—Theoretical Development." Journal of Biomechanical Engineering 113, no. 1 (February 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 activation through a shifting zero-stress configuration. Strain-displacement relations are given for the special case of axisymmetric deformation of shells of revolution with torsion.

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47

Elad, D., A. Foux, and Y. Kivity. "A Model for the Nonlinear Elastic Response of Large Arteries." Journal of Biomechanical Engineering 110, no. 3 (August 1, 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 (equivalent to Poisson’s ratios in infinitesimal deformations) are deformation dependent. This dependence is defined by empirical relations developed via the incompressibility condition, and by the introduction of a fifth material parameter. The resulting constitutive model compares well with biaxial experimental data of canine carotid arteries.

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48

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 (March 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, were analyzed. The experimental results illustrate that the average mass loss ratio of the corroded cable wires increases nonlinearly as corrosion time increases. The higher the stress level, the more serious the corrosion level. The minimum cross-sectional diameter has good correlation with corrosion time and stress level. The elastic modulus of wires does not change significantly with the increase of corrosion time. Yield load and ultimate load decreases with the increase of strain level, and the rates of decline under different strains are nonlinear.

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49

Orgill, G., and J. F. Wilson. "Finite Deformations of Nonlinear, Orthotropic Cylindrical Shells." Journal of Applied Mechanics 53, no. 2 (June 1, 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 dimensions and the constitutive law to account for geometric and material nonlinearities. Parametric studies show how the deformation behavior is influenced by the orientation of the angle of material orthotropy. Results may be applied to the design of pressure controlled robotic actuators and manipulators.

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50

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 (February 2, 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 method for the nonlinear dynamic problems of elasticity under finite strains is considered. Some details of parallel computing on multicore and multiprocessor systems for the problems of nonlinear dynamic elasticity are presented. The results of numerical experiments obtained in CAE Fidesys are shown, in particular: the analysis of propagation of nonlinear shock wave; the analysis of propagation of surface waves; the dynamic processes related with the origination of a hole in a weakly compressible nonlinear-viscoelastic material.</p>

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