Related papers: Third- and fourth-order elasticity of biological s…
Acousto-elasticity is concerned with the propagation of small-amplitude waves in deformed solids. Results previously established for the incremental elastodynamics of exact non-linear elasticity are useful for the determination of third-…
Classical acoustoelasticity couples small-amplitude elastic wave propagation to an infinitesimal pre-deformation, in order to reveal and evaluate non-destructively third-order elasticity constants. Here, we see that acoustoelasticity can be…
Consider the constitutive law for an isotropic elastic solid with the strain-energy function expanded up to the fourth order in the strain, and the stress up to the third order in the strain. The stress-strain relation can then be inverted…
Soft materials exhibit significant nonlinear geometric deformations and stress-strain relationships under external forces. This paper explores weakly nonlinear elasticity theories, including Landau's and Murnaghan's formulations, advancing…
The paper studies the interaction of a longitudinal wave with transverse waves in general isotropic and unconstrained hyperelastic materials, including the possibility of dissipation. The dissipative term chosen is similar to the classical…
Shear-wave elastography (SWE) measures shear-wave speed (SWS), which is related to the underlying shear modulus of soft tissue. SWE methods generally assume that soft tissue viscoelasticity is independent of mechanical loading, however,…
Using shear wave elastography, we measure the changes in the wave speed with the stress produced by a striated muscle during isometric voluntary contraction. To isolate the behaviour of an individual muscle from complementary or…
Identifying a universal material constitutive law, that describes the mechanical response of rubber-like solids for all deformation fields and achievable extensions, is an outstanding challenge. Here, we propose to exploit the propagation…
Quasicrystals can carry, in addition to the classical phonon displacement field, a phason displacement field, which requires a generalized theory of elasticity. In this paper, the third-order strain invariants (including phason strain) of…
Incompressibility is established for three-dimensional and two-dimensional deformations of an anisotropic linearly elastic material, as conditions to be satisfied by the elastic compliances. These conditions make it straightforward to…
This paper is concerned with an asymptotic analysis of the dispersion relation for wave propagation in an elastic layer of uniform thickness. The layer is subject to an underlying simple shear deformation accompanied by an arbitrary uniform…
Experiments on isotropic compression of a granular assembly of spheres show that the shear and bulk moduli vary with the confining pressure faster than the 1/3 power law predicted by Hertz-Mindlin effective medium theories (EMT) of contact…
Simple strain-rate viscoelasticity models of isotropic soft solid are introduced. The constitutive equations account for finite strain, incompressibility, material frame-indifference, nonlinear elasticity, and viscous dissipation. A…
Mechanical stress within biological tissue can indicate an anomaly, or can be vital of its function, such as stresses in arteries. Measuring these stresses in tissue is challenging due to the complex, and often unknown, nature of the…
Real-world solids, such as rocks, soft tissues, and engineering materials, are often under some form of stress. Most real materials are also, to some degree, anisotropic due to their microstructure, a characteristic often called the…
The strain-energy formulation of nonlinear elasticity can be extended to the case of significant compression by modulating suitable strain energy terms by a function of relative volume. For isotropic materials this can be accomplished by…
The development of a nonlinear structural theory (model) for isotropic linear-elastic finite continua is the main objective of the study. To derive the theory, we used Taylor's multivariable expansion and Bubnov-Galerkin's weak formulation.…
Many materials of contemporary interest, such as gels, biological tissues and elastomers, are easily deformed but essentially incompressible. Traditional linear theory of elasticity implements incompressibility only to first order and thus…
In this work we will derive an anisotropic generalisation of the finitely extensible chain model, due to Kuhn and Gr\"un, which is well known in rubber elasticity. This provides a chain energy that couples elastic behaviour to a probability…
In order to model nonlinear viscous dissipative motions in solids, acoustical physicists usually add terms linear in dot{E}, the material time derivative of the Lagrangian strain tensor E, to the elastic stress tensor sigma derived from the…