Related papers: Universal Deformations in Compressible Isotropic C…
For a given class of materials, \emph{universal deformations} are those deformations that can be maintained in the absence of body forces and by applying solely boundary tractions. For inhomogeneous bodies, in addition to the universality…
For a given material, \emph{controllable deformations} are those deformations that can be maintained in the absence of body forces and by applying only boundary tractions. For a given class of materials, \emph{universal deformations} are…
In this paper we study universal deformations in anisotropic Cauchy elasticity. We show that the universality constraints of hyperelasticity and Cauchy elasticity for transversely isotropic, orthotropic, and monoclinic solids are…
Universal deformations are those that can be maintained in the absence of body forces and with boundary tractions alone, for all materials within a given constitutive class. We study the universal deformations of compressible isotropic…
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…
In isotropic finite elasticity, unlike in the linear elastic theory, a homogeneous Cauchy stress may be induced by non-homogeneous strains. To illustrate this, we identify compatible non-homogeneous three-dimensional deformations producing…
On the basis of the nonlinear theory of elasticity, the general constitutive equation for an isotropic hyperelastic solid in the presence of initial stress is derived. This derivation involves invariants that couple the deformation with the…
It has recently been shown that for a Cauchy stress response induced by a strictly rank-one convex hyperelastic energy potential, a homogeneous Cauchy stress tensor field cannot correspond to a non-homogeneous deformation if the deformation…
Universal displacements are those displacements that can be maintained for any member of a specific class of linear elastic materials in the absence of body forces, solely by applying boundary tractions. For linear hyperelastic (Green…
Liquid crystal elastomers are rubber-like solids with liquid crystalline mesogens (stiff, rod-like molecules) incorporated either into the main chain or as a side chain of the polymer. These solids display a range of unusual…
For homogeneous, isotropic, nonlinearly elastic materials, the form of the homogeneous deformation consistent with the application of a Cauchy shear stress is derived here for both compressible and incompressible materials. It is shown that…
Residual stresses may appear in elastic bodies due to the formation of misfits in the micro-structure, driven by plastic deformations, thermal or growth processes. They are especially widespread in living matter, resulting from the dynamic…
In an interesting recent paper [1] (A. Acharya, Stress of a spatially uniform dislocation density field, J. Elasticity 137 (2019), 151--155), Acharya proved that the stress produced by a spatially uniform dislocation density field in a body…
In this paper we consider a sample of a linearly elastic heterogeneous composite in elastodynamic equilibrium and present universal theorems which provide lower bounds for the total elastic strain energy plus the kinetic energy, and the…
In a 2012 article in the International Journal of Non-Linear Mechanics, Destrade et al. showed that for nonlinear elastic materials satisfying Truesdell's so-called empirical inequalities, the deformation corresponding to a Cauchy pure…
We test some Hooke-like isotropic hyper-/hypo-elastic material models under finite simple shear deformations (cf., Thiel et al. Int. J. Non-linear Mech. 112: 57--72, 2019) and show that (1) the components of the Cauchy stress tensor for any…
In isotropic nonlinear elasticity the corotational stability postulate (CSP) is the requirement that \begin{equation*} \langle\frac{\mathrm{D}^{\circ}}{\mathrm{D} t}[\sigma] , D \rangle > 0 \quad \forall \ D \in \text{Sym}(3)\setminus \{0\}…
It can be shown that the stress produced by a spatially uniform dislocation density field in a body comprising a linear elastic material under no loads vanishes. We prove that the same result does not hold in general in the geometrically…
We derive the rate-form spatial equilibrium system for a nonlinear Cauchy elastic formulation in isotropic finite-strain elasticity. For a given explicit Cauchy stress-strain constitutive equation, we determine those properties that pertain…
The main result of this work is a homogenization theorem via variational convergence for elastic materials with stiff checkerboard-type heterogeneities under the assumptions of physical growth and non-self-interpenetration. While the…