Related papers: Elastic bounds for anisotropic layers
The perfectly matched layer is very important for the elastic wave problem in the frequency domain. Generally, the formulas of the elasticity tensor in the perfectly matched layers are derived from the transformed momentum equation. In this…
Lattice defects in crystalline materials create long-range elastic fields which can be modelled on the atomistic scale using an infinite system of discrete nonlinear force balance equations. Starting with these equations, this work…
An anisotropic elastic material is referred to as exotic when, under specific loadings, its mechanical response exhibits a higher degree of symmetry than that prescribed by its intrinsic material symmetry. Such materials, which may be…
The concepts of representative volume element (RVE), statistical homogeneity and homogeneous boundary conditions are invoked to arrive at bounds on effective moduli for heterogeneous anisotropic poroelastic solids. The homogeneous…
Helical ribbons arise in many biological and engineered systems, often driven by anisotropic surface stress, residual strain, and geometric or elastic mismatch between layers of a laminated composite. A full mathematical analysis is…
To begin with, we identify the equations of elastostatics in a Riemannian manifold, which generalize those of classical elasticity in the three-dimensional Euclidean space. Our approach relies on the principle of least energy, which asserts…
An infinite class of exact static anisotropic spheres is developed. All members of the class satisfy (i) regularity (meaning no singularities), and in particular at the origin, (ii) positive but monotone decreasing energy density…
In the framework of multiple-scattering theory, we show that the dispersion relations of certain electromagnetic (EM) and elastic metamaterials can be obtained analytically in the long-wavelength limit. Specific examples are given to the…
Based on the results published recently [SciPost Phys. 7, 026 (2019)], the influence of surfaces and boundary fields are calculated for the ferromagnetic anisotropic square lattice Ising model on finite lattices as well as in the…
A linear elastic circular disc is analyzed under a self-equilibrated system of loads applied along its boundary. A distinctive feature of the investigation, conducted using complex variable analysis, is the assumption that the material is…
This is a review of theoretical results from the three-dimensional equations of anisotropic elasticity or linear piezoelectricity on waves and vibrations in quartz crystal plates. It covers both the classical results on acoustic wave…
A numerical study on the elastic response of single- and multi-layer systems formed by alternating pentamode lattices and stiffening plates is presented. Finite element simulations are conducted to analyze the dependence of the effective…
This work is concerned with the purely dissipative version of a well-established model of rate-independent strain-gradient plasticity. In the conventional theory of plasticity the approach to determining plastic flow is local, and based on…
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…
We consider bound states in the continuum (BICs) in a 1D multilayered system of an anisotropic defect layer embedded into an anisotropic photonic crystal. We analytically demonstrate that an anisotropic defect layer embedded into…
There are many different formulations of relativistic elasticity. Most of them are only concerned with formal questions rather than questions regarding the PDE point of view. The aim of this thesis is to obtain various local existence…
In this note we present concrete applications of the general treatment of anisotropic thermo-elasticity developed in Part I.
We consider nonlinear viscoelastic materials of differential type and for some special models we derive exact solutions of initial boundary value problems. These exact solutions are used to investigate the reasons of non-existence of global…
The choice of elastic energies for thin plates and shells is an unsettled issue with consequences for much recent modeling of soft matter. Through consideration of simple deformations of a thin body in the plane, we demonstrate that four…
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…