Related papers: Non-Hookean elasticity with arbitrary Poisson's ra…
We find the strain energy function for isotropic incompressible solids exhibiting a linear relationship between shear stress and amount of shear, and between torque and amount of twist, when subject to large simple shear or torsion…
The lower bound usually cited for Poisson's ratio {\nu} is -1, derived from the relationship between {\nu} and the bulk and shear moduli. From consideration of the longitudinal and biaxial moduli, we recently determined that the lower bound…
As a service for the solid mechanics community we gather in this paper constitutive properties of a collective list of isotropic elastic energies for compressible materials. Of interest to us are the invertibility and monotonicity of…
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…
We discuss whether homogeneous Cauchy stress implies homogeneous strain in isotropic nonlinear elasticity. While for linear elasticity the positive answer is clear, we exhibit, through detailed calculations, an example with inhomogeneous…
Incompressible nonlinearly hyperelastic materials are rarely simulated in Finite Element numerical experiments as being perfectly incompressible because of the numerical difficulties associated with globally satisfying this constraint. Most…
We propose a nonlinear elasto-plastic model, for which a specific class of hyperbolic elasticity arises as a straight consequence of the yield criterion invariance on the plasticity level. We superimpose this nonlinear elastic (or…
Particle based methods such as the Discrete Element Method and the Lattice Spring Method may be used for describing the behaviour of isotropic linear elastic materials. However, the common bond models employed to describe the interaction…
Conditions for a maximum or minimum of Poisson's ratio of anisotropic elastic materials are derived. For a uniaxial stress in the 1-direction and Poisson's ratio $\nu$ defined by the contraction in the 2-direction, the following three…
The elastic moduli, elastic anisotropy coefficients, sound velocities and Poisson's ratio of hcp solid helium have been calculated using density functional theory in generalized gradient approximation (up to $30$ TPa), and pair+triple…
This study addresses the modelling of elastic bodies, particularly when the relaxed configuration is unknown or non-existent. We adopt the theory of initially stressed materials, incorporating the deformation gradient and stress state of…
Stochastic homogeneous hyperelastic solids are characterised by strain-energy densities where the parameters are random variables defined by probability density functions. These models allow for the propagation of uncertainties from input…
Dilational materials are stable three-dimensional isotropic auxetics with an ultimate Poisson's ratio of -1. We design, evaluate, fabricate, and characterize crystalline metamaterials approaching this ideal. To reveal all modes, we…
In this paper, we describe a uniform and standardized approach for analytically verifying the stability of isotropic, incompressible hyperelastic material models. Here, we address {\sl stability} as fulfillment of the {\sc Hill} condition…
We study the nonlinear elastic response of a two-dimensional material to a localized boundary force, with the particular goal of understanding the differences observed between isotropic granular materials and those with hexagonal…
An incremental (or tangent) bulk modulus for finite isotropic elasticity is defined which compares an increment in hydrostatic pressure with the corresponding increment in relative volume. Its positivity provides a stringent criterion for…
Physical experiments can characterize the elastic response of granular materials in terms of macroscopic state-variables, namely volume (packing) fraction and stress, while the microstructure is not accessible and thus neglected. Here, by…
A general expression for the strain energy of a homogeneous, isotropic, plane extensible elastica with an arbitrary undeformed configuration is derived. This energy constitutes the correct expression for one-dimensional models of polymers…
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…
This paper presents a theory for the behaviour of isotropic-hardening/softening elastoplastic materials that do not have a preferred reference configuration. In spite of important differences, many ingredients of classical plasticity are…