相关论文: On Universal Deformations and Material Preferred D…

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…

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…

We investigate universal deformations in compressible isotropic Cauchy elastic solids with residual stress, without assuming any specific source for the residual stress. We show that universal deformations must be homogeneous, and the…

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…

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 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…

For a given class of materials, universal displacements are those displacements that can be maintained for any member of the class by applying only boundary tractions. In this paper we study universal displacements in compressible…

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…

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…

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…

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…

Deformations of conventional solids are described via elasticity, a classical field theory whose form is constrained by translational and rotational symmetries. However, flexible metamaterials often contain an additional approximate…

We consider Cauchy's equation of motion for hyperelastic materials. The solution of this nonlinear initial-boundary value problem is the vector field which discribes the displacement which a particle of this material perceives when exposed…

We study elasticity of spontaneously orientationally-ordered amorphous solids, characterized by a vanishing transverse shear modulus, as realized for example by nematic elastomers and gels. We show that local heterogeneities and elastic…

In this note we develop tools to study the Cauchy problem for the system of thermo-elasticity in higher dimensions. The theory is developed for general homogeneous anisotropic media under non-degeneracy conditions. For degenerate cases a…

A law previously found for shear moduli of crystalline materials is developed and extended to all elastic moduli in solids and structures. Shear moduli were previously shown to depend only on specific volume. The bulk moduli of many…

The nonconservative elastic responses of active solids have driven a recent explosion of interest in two-dimensional "odd" elasticity: small, linear deformations of these Cauchy elastic solids enable new behaviour absent from classical,…

Universality in materials deformation is of intense interest: universal scaling relations if exist would bridge the gap from microscopic deformation to macroscopic response in a single material-independent fashion. While recent agreement of…

The Cauchy relations distinguish between rari- and multi-constant linear elasticity theories. These relations are treated in this paper in a form that is invariant under two groups of transformations: indices permutation and general linear…

We develop a molecular model of non-uniform deformations within the framework of liquid crystal rubber elasticity. We show that, similarly to the uniform case, the theory is not sensitive to the molecular details of polymer liquid crystal…