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Journal articles on the topic 'Linear elastic solids'

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Author: Grafiati

Published: 6 September 2023

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1

Wineman, Alan. "Mechanical Response of Linear Viscoelastic Solids." MRS Bulletin 16, no. 8 (August 1991): 19–23. http://dx.doi.org/10.1557/s088376940005627x.

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The word “viscoelastic” is used to describe the mechanical response of materials exhibiting both the springiness associated with elastic solids and viscous flow characteristics associated with fluids. A familiar example of a material called viscoelastic is Silly PuttyTM. If a blob of Silly Putty is rolled into a ball and then dropped onto a hard surface, it will bounce like an elastic ball. If the ball is placed on a hard surface, its own weight will cause it to flow into a puddle. This behavior indicates that time is an intrinsic parameter in discussing viscoelastic response of materials. The elastic response is associated with a contact force of very short duration. The flow into a puddle occurs when forces act for a long period of time.Viscoelastic response occurs in materials such as soils, concrete, cartilage, biological tissue, and polymers. Soils and cartilage can be thought of as porous solids filled with fluid. Viscous response is due to the flow of the fluid in the pores; elastic response is due to the distortion of the porous solid.

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2

Liu, Wenyang, and Jung Wuk Hong. "Discretized peridynamics for linear elastic solids." Computational Mechanics 50, no. 5 (February 25, 2012): 579–90. http://dx.doi.org/10.1007/s00466-012-0690-1.

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3

Ieşan, D., and R. Quintanilla. "Non-linear deformations of porous elastic solids." International Journal of Non-Linear Mechanics 49 (March 2013): 57–65. http://dx.doi.org/10.1016/j.ijnonlinmec.2012.08.005.

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4

Rudnicki, J. W. "Plane Strain Dislocations in Linear Elastic Diffusive Solids." Journal of Applied Mechanics 54, no. 3 (September 1, 1987): 545–52. http://dx.doi.org/10.1115/1.3173067.

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Solutions are obtained for the stress and pore pressure due to sudden introduction of plane strain dislocations in a linear elastic, fluid-infiltrated, Biot, solid. Previous solutions have required that the pore fluid pressure and its gradient be continuous. Consequently, the antisymmetry (symmetry) of the pore pressure p about y = 0 requires that this plane be permeable (p = 0) for a shear dislocation and impermeable (∂p/∂y = 0) for an opening dislocation. Here Fourier and Laplace transforms are used to obtain the stress and pore pressure due to sudden introduction of a shear dislocation on an impermeable plane and an opening dislocation on a permeable plane. The pore pressure is discontinuous on y = 0 for the shear dislocation and its gradient is discontinuous on y = 0 for the opening dislocation. The time-dependence of the traction induced on y = 0 is identical for shear and opening dislocations on an impermeable plane, but differs significantly from that for dislocations on a permeable plane. More specifically, the traction on an impermeable plane does not decay monotonically from its short-time (undrained) value as it does on a permeable plane; instead, it first increases to a peak in excess of the short-time value by about 20 percent of the difference between the short and long time values. Differences also occur in the distribution of stresses and pore pressure depending on whether the dislocations are emplaced on permeable or impermeable planes.

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5

Mei, Yue, and Sevan Goenezen. "Quantifying the anisotropic linear elastic behavior of solids." International Journal of Mechanical Sciences 163 (November 2019): 105131. http://dx.doi.org/10.1016/j.ijmecsci.2019.105131.

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6

Bennati, Stefano, and Cristina Padovani. "Some Non-linear Elastic Solutions for Masonry Solids*." Mechanics of Structures and Machines 25, no. 2 (January 1997): 243–66. http://dx.doi.org/10.1080/08905459708905289.

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7

Suárez-Antola, Roberto. "Power Law and Stretched Exponential Responses in Composite Solids." Advanced Materials Research 853 (December 2013): 9–16. http://dx.doi.org/10.4028/www.scientific.net/amr.853.9.

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Clay, rocks, concrete and other composite solids show evidence of a hierarchical structure. A fractal tree of nested viscoelastic boxes is proposed to describe the elastic after-effects in these composite solids. A generalized fractal transmission line approach is developed to relate the strain and stress responses. Power law for strain, under an applied stress step, is derived. The exponent in the power law is obtained as a well-defined function of the branching numbers and scaling parameters of the viscoelastic hierarchy. Then, a composite solid with both instantaneous (linear) elastic strain response and power law type (linear) elastic after-effect for an applied stress step, is considered. The stretched exponential stress relaxation to an applied strain step is derived as an approximation. For the same composite solid, the stretch parameter of the stretched exponential and the exponent of the power law result to be equal to each other.

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8

Sakai, M., T. Akatsu, S. Numata, and K. Matsuda. "Linear strain hardening in elastoplastic indentation contact." Journal of Materials Research 18, no. 9 (September 2003): 2087–96. http://dx.doi.org/10.1557/jmr.2003.0293.

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Finite-element analyses for elastoplastic cone indentations were conducted in which the effect of linear strain hardening on indentation behavior was intensively examined in relation to the influences of the frictional coefficient (μ) at the indenter/material contact interface and of the inclined face angle (β) of the cone indenter. A novel procedure of “graphical superposition” was proposed to determine the representative yield stress YR. It was confirmed that the concept of YR applied to elastic-perfectlyplastic solids is sufficient enough for describing the indentation behavior of strainhardening elastoplastic solids. The representative plastic strain of εR (plastic) ≈ 0.22 tan β, at which YR is prescribed, is applicable to the strain-hardening elastoplastic solids, affording a quantitative relationship of YR = Y + ε;R (plastic) × EP in terms of the strain-hardening modulus EP. The true hardness H as a measure for plasticity is estimated from the Meyer hardness HM and then successfully related to the yield stress Y as H = C(β,μ) × Y for elastic-perfectly-plastic solids and as H = C(β,μ) × YR for strain-hardening solids, by the use of a β- and μ-dependent constraint factor C(β,μ) ranging from 2.6 to 3.2.

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9

Angjeliu, Grigor, Matteo Bruggi, and Alberto Taliercio. "Analysis of Linear Elastic Masonry-Like Solids Subjected to Settlements." Key Engineering Materials 916 (April 7, 2022): 155–62. http://dx.doi.org/10.4028/p-dsufgb.

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A linear elastic no-tension material model is implemented in this contribution to cope with the analysis of masonry-like solids in case of either elastic or inelastic settlements. Instead of implementing an incremental non-linear approach, an energy-based method is adopted to address the elastic no-tension equilibrium. Under a prescribed set of compatible loads, and possible enforced displacements, a solution is found by distributing an equivalent orthotropic material having negligible stiffness in tension, such that the overall strain energy is minimized and the stress tensor is negative semi-definite all over the domain. A preliminary implementation of the proposed method is given by adopting a heuristic approach to turn the multi-constrained minimization problem into an unconstrained one. Numerical simulations focus on a wall with an opening subjected to either inelastic settlement or standing on elastic soil.

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10

Rafizadeh, H. A. "Complex force-constant dependence of elastic constants." Canadian Journal of Physics 68, no. 1 (January 1, 1990): 14–22. http://dx.doi.org/10.1139/p90-003.

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Expressions for the inner and bare components of the elastic constants of crystalline solids are derived. The inner elastic constants are complex functions of the force constants and vanish only for centrosymmetric solids. Using a linear-chain model, the force-constant dependence of inner, bare, and total elastic constants is studied. The linear-chain model is also utilized in derivation of composition-dependent elastic constant equations. Single-parameter and two-parameter theoretical calculations are compared with the experimental composition-dependent Young's moduli of a number of metal–metalloid glasses.

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11

Ciarletta, Michele, and Antonio Scalia. "Some Results in Linear Theory of Thermomicrostretch Elastic Solids." Meccanica 39, no. 3 (June 2004): 191–206. http://dx.doi.org/10.1023/b:mecc.0000022843.48821.af.

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12

Nachtrab, Susan, Sebastian C. Kapfer, Christoph H. Arns, Mahyar Madadi, Klaus Mecke, and Gerd E. Schröder-Turk. "Morphology and Linear-Elastic Moduli of Random Network Solids." Advanced Materials 23, no. 22-23 (June 16, 2011): 2633–37. http://dx.doi.org/10.1002/adma.201004094.

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13

Haghighi, Ehsan Motevali, and Seonhong Na. "A Multifeatured Data-Driven Homogenization for Heterogeneous Elastic Solids." Applied Sciences 11, no. 19 (October 3, 2021): 9208. http://dx.doi.org/10.3390/app11199208.

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A computational homogenization of heterogeneous solids is presented based on the data-driven approach for both linear and nonlinear elastic responses. Within the Double-Scale Finite Element Method (FE2) framework, a data-driven model is proposed to substitute the micro-level Finite Element (FE) simulations to reduce computational costs in multiscale simulations. The heterogeneity of porous solids at the micro-level is considered in various material properties and geometrical attributes. For material properties, elastic constants, which are Lame’s coefficients, are subjected to be heterogeneous in the linear elastic responses. For geometrical features, different numbers, sizes, and locations of voids are considered to reflect the heterogeneity of porous solids. A database for homogenized microstructural responses is constructed from a series of micro-level FE simulations, and machine learning is used to train and test our proposed model. In particular, four geometrical descriptors are designed, based on N-probability and lineal-path functions, to clearly reflect the geometrical heterogeneity of various microstructures. This study indicates that a simple deep neural networks model can capture diverse microstructural heterogeneous responses well when given proper input sources, including the geometrical descriptors, are considered to establish a computational data-driven homogenization scheme.

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14

Larionov, Egor, Ye Fan, and Dinesh K. Pai. "Frictional Contact on Smooth Elastic Solids." ACM Transactions on Graphics 40, no. 2 (April 20, 2021): 1–17. http://dx.doi.org/10.1145/3446663.

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Frictional contact between deformable elastic objects remains a difficult simulation problem in computer graphics. Traditionally, contact has been resolved using sophisticated collision detection schemes and methods that build on the assumption that contact happens between polygons. While polygonal surfaces are an efficient representation for solids, they lack some intrinsic properties that are important for contact resolution. Generally, polygonal surfaces are not equipped with an intrinsic inside and outside partitioning or a smooth distance field close to the surface. Here we propose a new method for resolving frictional contacts against deforming implicit surface representations that addresses these problems. We augment a moving least squares (MLS) implicit surface formulation with a local kernel for resolving contacts, and develop a simple parallel transport approximation to enable transfer of frictional impulses. Our variational formulation of dynamics and elasticity enables us to naturally include contact constraints, which are resolved as one Newton-Raphson solve with linear inequality constraints. We extend this formulation by forwarding friction impulses from one time step to the next, used as external forces in the elasticity solve. This maintains the decoupling of friction from elasticity thus allowing for different solvers to be used in each step. In addition, we develop a variation of staggered projections, that relies solely on a non-linear optimization without constraints and does not require a discretization of the friction cone. Our results compare favorably to a popular industrial elasticity solver (used for visual effects), as well as recent academic work in frictional contact, both of which rely on polygons for contact resolution. We present examples of coupling between rigid bodies, cloth and elastic solids.

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15

De Cicco, Simona, and Ludovico Nappa. "Some Results in the Linear Theory of Thermomicrostretch Elastic Solids." Mathematics and Mechanics of Solids 5, no. 4 (December 2000): 467–82. http://dx.doi.org/10.1177/108128650000500405.

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16

Wu, Kuang-Chong, Yu-Tsung Chiu, and Zhong-Her Hwu. "A New Boundary Integral Equation Formulation for Linear Elastic Solids." Journal of Applied Mechanics 59, no. 2 (June 1, 1992): 344–48. http://dx.doi.org/10.1115/1.2899526.

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A new boundary integral equation formulation is presented for two-dimensional linear elasticity problems for isotropic as well as anisotropic solids. The formulation is based on distributions of line forces and dislocations over a simply connected or multiply connected closed contour in an infinite body. Two types of boundary integral equations are derived. Both types of equations contain boundary tangential displacement gradients and tractions as unknowns. A general expression for the tangential stresses along the boundary in terms of the boundary tangential displacement gradients and tractions is given. The formulation is applied to obtain analytic solutions for half-plane problems. The formulation is also applied numerically to a test problem to demonstrate the accuracy of the formulation.

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17

Barnett, David M. "Bulk, surface, and interfacial waves in anisotropic linear elastic solids." International Journal of Solids and Structures 37, no. 1-2 (January 2000): 45–54. http://dx.doi.org/10.1016/s0020-7683(99)00076-1.

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18

Ranjith, K. "Dynamic anti-plane sliding of dissimilar anisotropic linear elastic solids." International Journal of Solids and Structures 45, no. 14-15 (July 2008): 4211–21. http://dx.doi.org/10.1016/j.ijsolstr.2008.03.002.

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19

Adams, M. J., D. Williams, and J. G. Williams. "The use of linear elastic fracture mechanics for particulate solids." Journal of Materials Science 24, no. 5 (May 1989): 1772–76. http://dx.doi.org/10.1007/bf01105704.

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20

Hwu, Chyanbin, J. Y. Wu, C. W. Fan, and M. C. Hsieh. "Stroh Finite Element for Two-Dimensional Linear Anisotropic Elastic Solids." Journal of Applied Mechanics 68, no. 3 (November 30, 2000): 468–75. http://dx.doi.org/10.1115/1.1364497.

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A general solution satisfying the strain-displacement relation, the stress-strain laws and the equilibrium conditions has been obtained in Stroh formalism for the generalized two-dimensional anisotropic elasticity. The general solution contains three arbitrary complex functions which are the basis of the whole field stresses and deformations. By selecting these arbitrary functions to be linear or quadratic, and following the direct finite element formulation, a new finite element satisfying both the compatibility and equilibrium within each element is developed in this paper. A computer windows program is then coded by using the FORTRAN and Visual Basic languages. Two numerical examples are shown to illustrate the performance of this newly developed finite element. One is the uniform stress field problem, the other is the stress concentration problem.

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21

Cheng, Yang-Tse, Wangyang Ni, and Che-Min Cheng. "Determining the Instantaneous Modulus of Viscoelastic Solids Using Instrumented Indentation Measurements." Journal of Materials Research 20, no. 11 (November 2005): 3061–71. http://dx.doi.org/10.1557/jmr.2005.0389.

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Instrumented indentation is often used in the study of small-scale mechanical behavior of “soft” matters that exhibit viscoelastic behavior. A number of techniques have recently been proposed to obtain the viscoelastic properties from indentation load–displacement curves. In this study, we examine the relationships between initial unloading slope, contact depth, and the instantaneous elastic modulus for instrumented indentation in linear viscoelastic solids using either conical or spherical indenters. In particular, we study the effects of “hold-at-the-peak-load” and “hold-at-the-maximum-displacement” on initial unloading slopes and contact depths. We then discuss the applicability of the Oliver–Pharr method (Refs. 29, 30) for determining contact depth that was originally proposed for indentation in elastic and elastic-plastic solids and recently modified by Ngan et al. (Refs. 20–23) for viscoelastic solids. The results of this study should help facilitate the analysis of instrumented indentation measurements in linear viscoelastic solids.

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22

Cheng, Yang-Tse, and Che-Min Cheng. "Relationships between initial unloading slope, contact depth, and mechanical properties for conical indentation in linear viscoelastic solids." Journal of Materials Research 20, no. 4 (April 1, 2005): 1046–53. http://dx.doi.org/10.1557/jmr.2005.0141.

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Using analytical and finite element modeling, we studied conical indentation in linear viscoelastic solids with either displacement or load as the independent variable. We examine the relationships between initial unloading slope, contact depth, and viscoelastic properties for various loading conditions such as constant displacement rate, constant loading rate, and constant indentation strain rate. We then discuss whether the Oliver–Pharr method for determining contact depth, originally proposed for indentation in elastic and elastic-plastic solids, is applicable to indentation in viscoelastic solids. We conclude with a few comments about two commonly used experimental procedures for indentation measurements in viscoelastic solids: the “hold-at-peak-load” technique and the constant indentation strain-rate method.

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23

Kumara P., Kirana, and Ashitava Ghosal. "Real-Time Computer Simulation of Three Dimensional Elastostatics Using the Finite Point Method." Applied Mechanics and Materials 110-116 (October 2011): 2740–45. http://dx.doi.org/10.4028/www.scientific.net/amm.110-116.2740.

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Real-time simulation of deformable solids is essential for some applications such as biological organ simulations for surgical simulators. In this work, deformable solids are approximated to be linear elastic, and an easy and straight forward numerical technique, the Finite Point Method (FPM), is used to model three dimensional linear elastostatics. Graphics Processing Unit (GPU) is used to accelerate computations. Results show that the Finite Point Method, together with GPU, can compute three dimensional linear elastostatic responses of solids at rates suitable for real-time graphics, for solids represented by reasonable number of points.

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24

Destrade, Michel, Edvige Pucci, and Giuseppe Saccomandi. "Generalization of the Zabolotskaya equation to all incompressible isotropic elastic solids." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475, no. 2227 (July 2019): 20190061. http://dx.doi.org/10.1098/rspa.2019.0061.

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We study elastic shear waves of small but finite amplitude, composed of an anti-plane shear motion and a general in-plane motion. We use a multiple scales expansion to derive an asymptotic system of coupled nonlinear equations describing their propagation in all isotropic incompressible nonlinear elastic solids, generalizing the scalar Zabolotskaya equation of compressible nonlinear elasticity. We show that for a general isotropic incompressible solid, the coupling between anti-plane and in-plane motions cannot be undone and thus conclude that linear polarization is impossible for general nonlinear two-dimensional shear waves. We then use the equations to study the evolution of a nonlinear Gaussian beam in a soft solid: we show that a pure (linearly polarized) shear beam source generates only odd harmonics, but that introducing a slight in-plane noise in the source signal leads to a second harmonic, of the same magnitude as the fifth harmonic, a phenomenon recently observed experimentally. Finally, we present examples of some special shear motions with linear polarization.

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25

Sanditov D.S. "Elastic properties and anharmonicity of solids." Physics of the Solid State 64, no. 2 (2022): 229. http://dx.doi.org/10.21883/pss.2022.02.52973.045.

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The squares of the velocities of the longitudinal and transverse acoustic waves separately are practically not associated with anharmonicity, and their ratio (νL2/νS2) turns out to be a linear function of the Gruneisen parameter γ --- the measure of anharmonicity. The obtained dependence of (νL2/νS2) on γ is in satisfactory agreement with the experimental data. The relationship between the quantity (νL2/νS2) and anharmonicity is explained through its dependence on the ratio of the tangential and normal stiffness of the interatomic bond λ, which is a single-valued function of the Gruneisen parameter λ(γ). The relationship between Poisson's ratio μ and Gruneisen parameter γ, established by Belomestnykh and Tesleva, can be substantiated within the framework of Pineda's theory. Attention is drawn to the nature of the Leont'ev formula, derived directly from the definition of the Gruneisen parameter by averaging the frequency of normal lattice vibration modes. The connection between Gruneisen, Leontiev and Belomestnykh--Tesleva relations is considered. The possibility of a correlation between the harmonic and anharmonic characteristics of solids is discussed. Keywords: elastic properties, Gruneisen parameter, formulas of Belomestnykh--Tesleva, Leont'ev, Gruneisen equation, tangential and normal stiffness of interatomic bond, crystals, glasses.

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26

Nemat-Nasser, Sia, and Muneo Hori. "Universal Bounds for Overall Properties of Linear and Nonlinear Heterogeneous Solids." Journal of Engineering Materials and Technology 117, no. 4 (October 1, 1995): 412–32. http://dx.doi.org/10.1115/1.2804735.

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For a sample of a general heterogeneous nonlinearly elastic material, it is shown that, among all consistent boundary data which yield the same overall average strain (stress), the strain (stress) field produced by uniform boundary tractions (linear boundary displacements), renders the elastic strain (complementary strain) energy an absolute minimum. Similar results are obtained when the material of the composite is viscoplastic. Based on these results, universal bounds are presented for the overall elastic parameters of a general, possibly finite-sized, sample of heterogeneous materials with arbitrary microstructures, subjected to any consistent boundary data with a common prescribed average strain or stress. Statistical homogeneity and isotropy are neither required nor excluded. Based on these general results, computable bounds are developed for the overall stress and strain (strain-rate) potentials of solids of any shape and inhomogeneity, subjected to any set of consistent boundary data. The bounds can be improved by incorporating additional material and geometric data specific to the given finite heterogeneous solid. Any numerical (finite-element or boundary-element) or analytical solution method can be used to analyze any subregion under uniform boundary tractions or linear boundary displacements, and the results can be incorporated into the procedure outlined here, leading to exact bounds. These bounds are not based on the equivalent homogenized reference solid (discussed in Sections 3 and 4). They may remain finite even when cavities or rigid inclusions are present. Complementary to the above-mentioned results, for linear cases, eigenstrains and eigenstresses are used to homogenize the solid, and general exact bounds are developed. In the absence of statistical homogeneity, the only requirement is that the overall shape of the sample be either parallelepipedic (rectangular or oblique) or ellipsoidal, though the size and relative dimensions of the sample are arbitrary. Then, exact analytically computable, improvable bounds are developed for the overall moduli and compliances, without any further assumptions or approximations. Bounds for two elastic parameters are shown to be independent of the number of inhomogeneity phases, and their sizes, shapes, or distribution. These bounds are the same for both parallelepipedic and ellipsoidal overall sample geometries, as well as for the statistically homogeneous and isotropic distribution of inhomogeneities. These bounds are therefore universal. The same formalism is used to develop universal bounds for the overall non-mechanical (such as thermal, diffusional, or electrostatic) properties of heterogeneous materials.

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27

Kurt, E., and M. S. Dokuz. "Load Ratios Carried by Each Constituent for Some Problems of a Particulate Composite Modeled as a Mixture of Two Linear Elastic Solids." Journal of Mechanics 36, no. 6 (October 14, 2020): 857–65. http://dx.doi.org/10.1017/jmech.2020.51.

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ABSTRACTThe basic constitutive equations of theory of mixtures obtained for a mixture of two linear elastic solids can be used as an alternative way to describe the mechanical behavior of binary composite materials. Determining the load ratios carried by each constituent solid of a binary composite is one of challenges of this theory. In this study, the results of directly calculating the ratios of external load carried by each constituent solid for the case of perfectly bonded interface between binary mixture constituents are discussed. Thus, the effects of loading type and volume fraction of the constituent solids to the load ratios carried by each constituent solid are investigated by using three different loading cases and three different volume fractions. Finally, displacement, stress and diffusive force results of two constituent solids using the calculated load ratios are given.

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28

Rudnicki, J. W., and E. A. Roeloffs. "Plane-Strain Shear Dislocations Moving Steadily in Linear Elastic Diffusive Solids." Journal of Applied Mechanics 57, no. 1 (March 1, 1990): 32–39. http://dx.doi.org/10.1115/1.2888320.

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This paper derives the stress and pore pressure fields induced by a plane-strain shear (gliding edge) dislocation moving steadily at a constant speed V in a linear elastic, fluid-infiltrated (Biot) solid. Solutions are obtained for the limiting cases in which the plane containing the moving dislocation (y = 0) is permeable and impermeable to the diffusing species. Although the solutions for the permeable and impermeable planes are required to agree with each other and with the ordinary elastic solution in the limits of V = 0 (corresponding to drained response) and V = ∞ (corresponding to undrained response), the stress and pore pressure fields differ considerably for finite nonzero velocities. For the dislocation on the impermeable plane, the pore pressure is discontinuous on y = 0 and attains values which are equal in magnitude and opposite in sign as y = 0 is approached from above and below. The solution reveals the surprising result that the pore pressure on the impermeable plane is zero everywhere behind the moving dislocation (x < 0). For the dislocation on the permeable plane, the pore pressure is zero on y = 0 and attains its maximum at about (2c/V, 2c/V) where c is the diffusivity, and the origin of the coordinate system coincides with the dislocation. For the impermeable plane, the largest pore pressure change occurs at the origin.

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29

Zhang, Yong, and Pizhong Qiao. "An axisymmetric ordinary state-based peridynamic model for linear elastic solids." Computer Methods in Applied Mechanics and Engineering 341 (November 2018): 517–50. http://dx.doi.org/10.1016/j.cma.2018.07.009.

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30

Rudnicki, John W. "Fluid mass sources and point forces in linear elastic diffusive solids." Mechanics of Materials 5, no. 4 (December 1986): 383–93. http://dx.doi.org/10.1016/0167-6636(86)90042-6.

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31

Borrelli, Alessandra, and Maria Cristina Patria. "Acceleration waves through a mixture of two non-linear elastic solids." Acta Mechanica 57, no. 1-2 (October 1985): 25–40. http://dx.doi.org/10.1007/bf01176672.

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32

SZEPTYŃSKI, Paweł. "DIRECTIONS OF EXTREME STIFFNESS AND STRENGTH IN LINEAR ELASTIC ANISOTROPIC SOLIDS." Mechanics and Control 31, no. 3 (2012): 124. http://dx.doi.org/10.7494/mech.2012.31.3.124.

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33

Boolakee, Oliver, Martin Geier, and Laura De Lorenzis. "A new lattice Boltzmann scheme for linear elastic solids: periodic problems." Computer Methods in Applied Mechanics and Engineering 404 (February 2023): 115756. http://dx.doi.org/10.1016/j.cma.2022.115756.

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34

Paccola, Rodrigo Ribeiro, Dorival Piedade Neto, and Humberto Breves Coda. "Geometrical non-linear analysis of fiber reinforced elastic solids considering debounding." Composite Structures 133 (December 2015): 343–57. http://dx.doi.org/10.1016/j.compstruct.2015.07.097.

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35

Yu, H. Y., and Sanboh Lee. "Time-harmonic elastic singularities and oscillating indentation of layered solids." IMA Journal of Applied Mathematics 85, no. 4 (June 8, 2020): 542–63. http://dx.doi.org/10.1093/imamat/hxaa017.

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Abstract A new approach is proposed for obtaining the dynamic elastic response of a multilayered elastic solid caused by axisymmetric, time-harmonic elastic singularities. The method for obtaining the elastodynamic Green’s functions of the point force, double forces and center of dilatation is presented. For this purpose, the boundary conditions in an infinite solid at the plane passing through the singularity are derived first by using Helmholtz potentials. Then the Green’s function solution for layered solids is obtained by solving a set of simultaneous linear algebraic equations using the boundary conditions for both the singularities and for the layer interfaces. The application of the point force solution for the oscillating normal indentation problem is also given. The solution of the forced normal oscillation is formulated by integrating the point force Green’s function over the contact area with unknown surface traction. The dual integral equations of the unknown surface traction are established by considering the boundary conditions on the contact surface of the multilayered solid, which can be converted into a Fredholm integral equation of the second kind and solved numerically.

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36

Wünsche, Michael, Chuan Zeng Zhang, Jan Sladek, Vladimir Sladek, and Sohichi Hirose. "Interface Crack in Anisotropic Solids under Impact Loading." Key Engineering Materials 348-349 (September 2007): 73–76. http://dx.doi.org/10.4028/www.scientific.net/kem.348-349.73.

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In this paper, transient dynamic crack analysis in two-dimensional, layered, anisotropic and linear elastic solids is presented. For this purpose, a time-domain boundary element method (BEM) is developed. The homogeneous and anisotropic layers are modeled by the multi-domain BEM formulation. Time-domain elastodynamic fundamental solutions for linear elastic and anisotropic solids are applied in the present BEM. The spatial discretization of the boundary integral equations is performed by a Galerkin-method while a collocation method is implemented for the temporal discretization of the arising convolution integrals. An explicit time-stepping scheme is developed to compute the discrete boundary data and the crack-opening-displacements (CODs). To show the effects of the material anisotropy and the dynamic loading on the dynamic stress intensity factors, numerical examples are presented and discussed.

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LIU, ZHANFANG, XIAOYONG SUN, and YUAN GUO. "ON ELASTIC STRESS WAVES IN AN IMPACTED PLATE." International Journal of Applied Mechanics 06, no. 04 (July 9, 2014): 1450047. http://dx.doi.org/10.1142/s1758825114500471.

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Elastic stress wave theory is developed and the stress waves in the impacted plate are examined in the paper. Generalized linear elasticity is adopted where the couple stress and curvature tensor are both deviatoric tensors and they meet a linear constitutive relation. It is found that there exist volumetric, rotational, and deviatoric waves in the generalized elastic solids. However, for macro-scale elastic solids only two wave modes, namely a volumetric wave and a deviatoric wave should be taken into account. Wave motion in plate impact tests is studied that a volumetric wave and a deviatoric wave are proposed. A set of exact solutions is attained for elastic stress waves in an impact plate. Excitation of stress waves at impact surface and reflection at free surface are formulated. Propagation of stress waves in the plate is analyzed in the waveforms. The predicted stress history in a ceramic plate under impact is agreed very well with the experiment measurement.

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Dimitrovova´, Z. "Effective Constitutive Properties of Linear Elastic Cellular Solids With Randomly Oriented Cells." Journal of Applied Mechanics 66, no. 4 (December 1, 1999): 918–25. http://dx.doi.org/10.1115/1.2791798.

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A new methodology to derive the linear effective constitutive law for a group of composites with random microstructure of a special kind is described as an extension of the methodology proposed in Warren and Kraynik (1988) and of the methodology used in polycrystal theory. The results are expressed in the form of specific bounds on effective elastic constants. Practical importance is in the specific bounds when the methodology is applied to cellular solids. Several examples are shown and compared with other published results. The new contribution of this paper lies in the presentation of the methodology, derivation of new specific bounds in two dimensions, and comments related to already published works on cellular solids.

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Harabagiu, Livia, and Olivian Simionescu-Panait. "Propagation of inhomogeneous plane waves in isotropic solid crystals." Analele Universitatii "Ovidius" Constanta - Seria Matematica 23, no. 3 (November 1, 2015): 55–64. http://dx.doi.org/10.1515/auom-2015-0047.

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Abstract In this paper we study the impact of initial mechanical deformation and electric fields applied to linear elastic isotropic solid, on the propagation of inhomogeneous plane waves in such media. We derive the decomposition of the propagation condition for particular isotropic directional bivectors and we show that the specific coefficients are similar to the case of guided waves propagation in isotropic solids subject to a bias.

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40

Theocaris, P. S., and T. P. Philippidis. "True bounds on Poisson's ratios for transversely isotropic solids." Journal of Strain Analysis for Engineering Design 27, no. 1 (January 1, 1992): 43–44. http://dx.doi.org/10.1243/03093247v271043.

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The basic principle of positive strain energy density of an anisotropic linear or non-linear elastic solid imposes bounds on the values of the stiffness and compliance tensor components. Although rational mathematical structuring of valid intervals for these components is possible and relatively simple, there are mathematical procedures less strictly followed by previous authors, which led to an overestimation of the bounds and misinterpretation of experimental results.

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Geubelle, P. H., and W. G. Knauss. "Crack Propagation at and Near Bimaterial Interfaces: Linear Analysis." Journal of Applied Mechanics 61, no. 3 (September 1, 1994): 560–66. http://dx.doi.org/10.1115/1.2901496.

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The problem of the growth of a crack located at the interface between two linearly elastic solids is considered when conditions promoting propagation along and/or away from the interface prevail. Both a stress and a maximum energy release rate criterion are examined. It is found that in contrast to the corresponding problem for crack growth in homogeneous solids, no unique propagation direction results when continuum considerations prevail alone. Uniqueness is established only upon invoking a presumably material dictated minimum crack extension size. The result for this linearized analysis are compared with experimental observations on kink fracture involving two elastomers of small strain capabilities.

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Pandey, Anupam, Stefan Karpitschka, Cornelis H. Venner, and Jacco H. Snoeijer. "Lubrication of soft viscoelastic solids." Journal of Fluid Mechanics 799 (June 23, 2016): 433–47. http://dx.doi.org/10.1017/jfm.2016.375.

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Lubrication flows appear in many applications in engineering, biophysics and nature. Separation of surfaces and minimisation of friction and wear is achieved when the lubricating fluid builds up a lift force. In this paper we analyse soft lubricated contacts by treating the solid walls as viscoelastic: soft materials are typically not purely elastic, but dissipate energy under dynamical loading conditions. We present a method for viscoelastic lubrication and focus on three canonical examples, namely Kelvin–Voigt, standard linear and power law rheology. It is shown how the solid viscoelasticity affects the lubrication process when the time scale of loading becomes comparable to the rheological time scale. We derive asymptotic relations between the lift force and the sliding velocity, which give scaling laws that inherit a signature of the rheology. In all cases the lift is found to decrease with respect to purely elastic systems.

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Imam, A., and G. C. Johnson. "Decomposition of the Deformation Gradient in Thermoelasticity." Journal of Applied Mechanics 65, no. 2 (June 1, 1998): 362–66. http://dx.doi.org/10.1115/1.2789063.

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The deformation gradient of a thermoelastic solid undergoing large deformations is decomposed into elastic and thermal components, corresponding to an intermediate configuration which is assumed to be stress-free. This decomposition is shown to be unique only to within a rigid-body motion of the intermediate configuration. An alternate decomposition is proposed in which this arbitrariness is removed. The thermoelastic theory developed on the basis of these decompositions is linearized, resulting in familiar expressions of linear thermoelasticity. The stress response function is further specialized for the particular case of isotropic linear solids.

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Kim, Jae Hun, and Andrew Gouldstone. "Spherical indentation of a membrane on an elastic half-space." Journal of Materials Research 23, no. 8 (August 2008): 2212–20. http://dx.doi.org/10.1557/jmr.2008.0278.

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A number of physiological systems involve contact or indentation of solids with tensed surface layers. In this paper the contact problem of spherical indentation of a linear elastic solid, covered with a tensed membrane is addressed. Semianalytical solutions are obtained relating indentation force to contact radius, as well as contact radius to depth. Good agreement is found between derived equations and results from finite element method (FEM) simulations. In addition, effect of membrane on subsurface stresses is shown quantitatively and compared favorably to FEM results. This work is applicable to mechanical property assessment of a number of biological systems.

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Svanadze, Merab. "Steady vibration problems in the coupled linear theory of porous elastic solids." Mathematics and Mechanics of Solids 25, no. 3 (November 28, 2019): 768–90. http://dx.doi.org/10.1177/1081286519888970.

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This paper concerns the coupled linear theory of elasticity for isotropic porous materials. In this theory the coupled phenomena of the concepts of Darcy’s law and the volume fraction is considered. The basic internal and external boundary value problems (BVPs) of steady vibrations are investigated. Indeed, the fundamental solution of the system of steady vibration equations is constructed explicitly by means of elementary functions, and its basic properties are presented. The radiation conditions are established and Green’s identities are obtained. The uniqueness theorems for the regular (classical) solutions of the BVPs are proved. The surface (single layer and double layer) and volume potentials are constructed and the basic properties of these potentials are given. Finally, the existence theorems for classical solutions of the BVPs are proved by means of the potential method (boundary integral equation method) and the theory of singular integral equations.

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Zelenina, A. A., and L. M. Zubov. "The non-linear theory of the pure bending of prismatic elastic solids." Journal of Applied Mathematics and Mechanics 64, no. 3 (January 2000): 399–406. http://dx.doi.org/10.1016/s0021-8928(00)00062-9.

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Ting, T. "The three-dimensional elastostatic Green's function for general anisotropic linear elastic solids." Quarterly Journal of Mechanics and Applied Mathematics 50, no. 3 (August 1, 1997): 407–26. http://dx.doi.org/10.1093/qjmam/50.3.407.

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Domański, Włodzimierz. "Propagation and interaction of non-linear elastic plane waves in soft solids." International Journal of Non-Linear Mechanics 44, no. 5 (June 2009): 494–98. http://dx.doi.org/10.1016/j.ijnonlinmec.2008.12.006.

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Borrelli, A., and M. C. Patria. "Acceleration waves through an isotropic mixture of two non-linear elastic solids." Acta Mechanica 67, no. 1-4 (May 1987): 91–106. http://dx.doi.org/10.1007/bf01182124.

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Fafalis, Dimitrios, and Jacob Fish. "Computational continua for linear elastic heterogeneous solids on unstructured finite element meshes." International Journal for Numerical Methods in Engineering 115, no. 4 (May 4, 2018): 501–30. http://dx.doi.org/10.1002/nme.5814.

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