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Linear elasticity
About: Linear elasticity is a research topic. Over the lifetime, 9080 publications have been published within this topic receiving 258684 citations.
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TL;DR: The aim of this study is to provide a review of constitutive equations based on the continuum mechanics approach for modelling the rate-independent mechanical behaviour of homogeneous, isotropic and incompressible biological materials.
Abstract: Modelling the mechanical behaviour of biological tissues is of vital importance for clinical applications. It is necessary for surgery simulation, tissue engineering, finite element modelling of soft tissues, etc. The theory of linear elasticity is frequently used to characterise biological tissues; however, the theory of nonlinear elasticity using hyperelastic models, describes accurately the nonlinear tissue response under large strains. The aim of this study is to provide a review of constitutive equations based on the continuum mechanics approach for modelling the rate-independent mechanical behaviour of homogeneous, isotropic and incompressible biological materials. The hyperelastic approach postulates an existence of the strain energy function--a scalar function per unit reference volume, which relates the displacement of the tissue to their corresponding stress values. The most popular form of the strain energy functions as Neo-Hookean, Mooney-Rivlin, Ogden, Yeoh, Fung-Demiray, Veronda-Westmann, Arruda-Boyce, Gent and their modifications are described and discussed considering their ability to analytically characterise the mechanical behaviour of biological tissues. The review provides a complete and detailed analysis of the strain energy functions used for modelling the rate-independent mechanical behaviour of soft biological tissues such as liver, kidney, spleen, brain, breast, etc.
73 citations
TL;DR: A thorough review of the main advances concerning both linear and nonlinear wave propagations in magnetizable deformable solids is presented in this paper, where the main features such as the influence of strong bias magnetic fields and the introduction of small parameters which bring corrections to classical results of elasticity theory are systematically investigated.
73 citations
TL;DR: In this paper, the authors examined the role of crack-tip conditions in the reduction of stress at a crack tip in a theory of linear elasticity with surface effects, and the maximum number of allowable end conditions for complete removal of a stress singularity is demonstrated for both plane and anti-plane problems.
Abstract: We examine the role of crack-tip conditions in the reduction of stress at a crack tip in a theory of linear elasticity with surface effects. The maximum number of allowable end conditions for complete removal of a stress singularity is demonstrated for both plane and anti-plane problems. In particular, we show that the necessary and sufficient conditions for bounded stresses at a crack tip cannot be satisfied with a first-order (curvature-independent) theory of surface effects, which leads, at most, to the reduction of the classical strong square-root singularity to a weaker logarithmic singularity.
73 citations
TL;DR: An extension of the discrete element modeling (DEM) approach, or clustered DEM, was used to simulate the hollow cylinder tensile (HCT) test, in which various material phases (e.g., aggregates, mastic) are modeled with bonded clusters of discrete elements as mentioned in this paper.
Abstract: An extension of the discrete element modeling (DEM) approach, or clustered DEM, was used to simulate the hollow cylinder tensile (HCT) test, in which various material phases (e.g., aggregates, mastic) are modeled with bonded clusters of discrete elements. The basic principle of the HCT test is the application of internal pressure to the inner cavity of a hollow cylinder specimen, which produces circumferential strain. In the present study an experimental program was conducted to measure the complex modulus of asphalt concrete mixtures at various loading rates and temperatures. The HCT test was then modeled with a two-dimensional, linear elastic DEM simulation. The current approach uses the correspondence principle to bridge between the elastic simulation and viscoelastic response. The two-dimensional morphology of the asphalt concrete mixture was captured with a high-resolution scanner, enhanced with image-processing techniques, and reconstructed into an assembly of discrete elements. The mixture complex moduli predicted in the HCT simulations were found to be in good agreement with experimental measurements across a range of test temperatures and loading frequencies for the coarse-grained mixtures investigated. Ongoing work in the area of viscoelastic constitutive modeling, fracture modeling, and three-dimensional tomography and modeling will extend the capabilities of this promising technique for fundamental studies of asphalt concrete and other particulate composites.
73 citations
01 Jan 2012
TL;DR: The mean compliance minimization in structural topology optimization is solved with the help of a phase field approach and the resulting flows are given by Allen-Cahn and Cahn-Hilliard type dynamics coupled to a linear elasticity system.
Abstract: The mean compliance minimization in structural topology optimization is solved with the help of a phase field approach. Two steepest descent approaches based on L2- and H-1-gradient flow dynamics are discussed. The resulting flows are given by Allen-Cahn and Cahn-Hilliard type dynamics coupled to a linear elasticity system. We finally compare numerical results obtained from the two different approaches.
73 citations