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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 present the foundations of a projective geometric theory of elasticity, as well as outline a few possible application possibilities. We give the description of the Cauchy stress and infinitesimal strain tensors compatible with coordinate…
Energies and equilibrium equations for thin elastic plates are discussed, with emphasis on several issues pertinent to recent approaches in soft condensed matter. Consequences of choice of basis, choice of invariant strain measures, and of…
We extend the theory of structured deformations to the setting of linearized elasticity by providing an integral representation for the underlying energy that features bulk and surface contributions. Our derivation is obtained both via a…
We study stationary points of the bending energy of curves $\gamma\colon[a,b]\to\mathbb{R}^n$ subject to constraints on the arc-length and the curve's holonomy while simultaneously allowing for a variable bending stiffness along the…
A general expression for the elastic potential energy of a helical spring is derived using the basic concepts of elasticity theory and geometry. Both the translational and the rotational displacement of the spring's moving ends are…
We derive an expression of the core traction contribution to the dislocation elastic energy within linear anisotropic elasticity theory using the sextic formalism. With this contribution, the elastic energy is a state variable consistent…
Integral expressions are determined for the elastic displacement and stress fields due to stationary or moving dislocation loops in three dimensional, not necessarily isotropic, finite samples. A line integral representation is found for…
Recently, a non-linear model of viscoelasticity based on Rational Extended Thermodynamics was proposed in [arXiv:2312.05116]. This theory extends the evolution of the viscous stress beyond the linear framework of the Maxwell model to the…
A thermodynamically consistent visco-elastodynamical model at finite strains is derived that also allows for inelasticity (like plasticity or creep), thermal coupling, and poroelasticity with diffusion. The theory is developed in the…
Polyconvexity is one of the known conditions which guarantee existence of solutions of boundary value problems in finite elasticity. In this work we propose a framework for development of polyconvex strain energy functions for hyperelastic…
In this article, we prove that solutions to a problem in nonlinear elasticity corresponding to small initial displacements exist globally in the exterior of a nontrapping obstacle. The medium is assumed to be homogeneous, isotropic, and…
A quasistatic model for a horizontally loaded thin elastic composite at small strains is studied. The composite consists of two adjacent plates whose interface behaves in a cohesive fashion with respect to the slip of the two layers. We…
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…
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 this paper we present a new general framework for anisotropic elastoplasticity at large strains. The new framework presents the following characteristics: (1) It is valid for non-moderate large strains, (2) it is valid for both elastic…
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…
Randomly textured polycrystalline materials of constituents with highly anisotropic nature of grains can be considered globally isotropic. In order to determine the isotropic properties, like elasticity or conductivity, we propose a theory…
We propose a model for nonlinearly elastic membranes undergoing finite deformations while confined to a regular frictionless surface in $\mathbb{R}^3$. This is a physically correct model of the analogy sometimes given to motivate harmonic…
A variational model for epitaxially-strained thin films on rigid substrates is derived both by {\Gamma}-convergence from a transition-layer setting, and by relaxation from a sharp-interface description available in the literature for…