Related papers: Optimal orientation of anisotropic solids
The ratio of directional strength-to-stiffness is important in governing the relative order in which individual crystals within a polycrystalline aggregate will yield as the aggregate is loaded. In this paper, a strength-to-stiffness…
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…
The paper is concerned with the Einstein equations for a spherically symmetric static distribution of anisotropic matter. The equations are cast into a system of Fuchsian type ODE for certain scalar invariants of the strain. And then the…
When solving the equations of General Relativity in a symmetric sector, it is natural to consider the same symmetry for the geometry and stress-energy. This implies that for static and isotropic spacetimes, the most general natural…
For the permittivity tensor of photoelastic anisotropic crystals we obtain the exact non-linear dependence on the Cauchy stress tensor. We obtain the same result for its square root whose principal components, the crystal principal…
We introduce a fundamental restriction on the strain energy function and stress tensor for initially stressed elastic solids. The restriction applies to strain energy functions $W$ that are explicit functions of the elastic deformation…
We consider anisotropic fluids with directional pressures $p_i = w_i \rho$ ($\rho$ is the density, $w_i = $const, $i = 1,2,3$) as sources of gravity in stationary cylindrically symmetric space-times. We describe a general way of obtaining…
In a recent series of papers new exact analytical solutions of Einstein equations representing interior spacetimes sourced by stationary rigidly rotating cylinders of fluids have been displayed. We have first considered a fluid with an…
Nematic liquid crystals in a polyhedral domain, a prototype for bistable displays, may be described by a unit-vector field subject to tangent boundary conditions. Here we consider the case of a rectangular prism. For configurations with…
The present paper completes our earlier results on nonlinear stability of stationary solutions of the Vlasov-Poisson system in the stellar dynamics case. By minimizing the energy under a mass-Casimir constraint we construct a large class of…
The tetragonal states produced by isotropic pseudomorphic epitaxial strain in the (001) plane on a tetragonal phase of a crystal are calculated for V, Ti, Rb, Li, K, Sr from first-principles electronic theory. It is shown that each metal…
The modelling of off-axis simple tension experiments on transversely isotropic nonlinearly elastic materials is considered. A testing protocol is proposed where normal force is applied to one edge of a rectangular specimen with the opposite…
An investigation of interior spacetimes sourced by stationary cylindrical anisotropic fluids is presented and specialized to rigidly rotating fluids with an azimuthally directed pressure. Based on the occurence of an extra degree of freedom…
This paper introduces a model for the mechanical response of anisotropic soft materials undergoing large inelastic deformations. The composite is constituted by a soft isotropic matrix reinforced with stiff fibres, that can evolve…
The polyconvexity of a strain-energy function is nowadays increasingly presented as the ultimate material stability condition for an idealized elastic response. While the mathematical merits of polyconvexity are clearly understood, its…
Integral expressions are determined for the elastic displacement and stress fields due to stationary or moving dislocation loops in finite samples. These general expressions are valid for anisotropic media as well. Specifically for the…
Mechanical and elastic properties of materials are among the most fundamental quantities for many engineering and industrial applications. Here, we present a formulation that is efficient and accurate for calculating the elastic and bending…
The nonlinear mechanics of a flexible elastic rod constrained at its edges by a pair of sliding sleeves is analyzed. The planar equilibrium configurations of this variable-length elastica are found to have shape defined only by the…
The paper is concerned with an optimal control problem governed by the equations of elasto plasticity with linear kinematic hardening and the inertia term at small strain. The objective is to optimize the displacement field and plastic…
Measurements of the resistivity anisotropy can provide crucial information about the electronic structure and scattering processes in anisotropic and low-dimensional materials, but quantitative measurements by conventional means often…