Related papers: Elastic bounds for anisotropic layers
We consider a free-boundary problem for the incompressible elastodynamics describing the motion of an elastic medium in a periodic domain with a moving boundary and a fixed bottom under the influence of surface tension. The local…
We study the spectral linear elasticity problem in an unbounded periodic waveguide, which consists of a sequence of identical bounded cells connected by thin ligaments of diameter of order $ h >0$. The essential spectrum of the problem is…
A new approach was recently introduced by the authors for constructing analytic solutions of the linear PDEs describing elastodynamics. Here, this approach is applied to the case of a homogeneous isotropic half-space body satisfying…
We consider an adhesive contact between a thin soft layer on a rigid substrate and a rigid cylindrical indenter ("line contact") with account of the surface tension of the layer. First, it is shown that the boundary condition for the…
We study, both analytically and numerically, the dynamics of elastic boundaries such as crack fronts in fracture and surfaces of contact in solid on solid friction. The elastic waves in the solid give rise to kinks that move with a…
Non-Euclidean plates are thin elastic bodies having no stress-free configuration, hence exhibiting residual stresses in the absence of external constraints. These bodies are endowed with a three-dimensional reference metric, which may not…
Biological cells in soft materials can be modeled as anisotropic force contraction dipoles. The corresponding elastic interaction potentials are long-ranged ($\sim 1/r^3$ with distance $r$) and depend sensitively on elastic constants,…
The inclusion of rigid elements into elastic composites may lead to superior mechanical properties for the equivalent elastic continuum, such as, for instance, extreme auxeticity. To allow full exploitation of these properties, a tool for…
We introduce the concept of basis for a lattice. This basis plays a vital role to determine the completeness and consistency of the lattice. Weighted lattices are introduced and its complexity is formulated. Some axiomatic systems,…
The analysis of the mathematical and mechanical properties of thermoelastic coupling tensors in anisotropic laminates is the topic of this paper. Some theoretical results concerning the compliance tensors are shown and their mechanical…
The paper establishes exact lower bound on the effective elastic energy of two-dimensional, three-material composite subjected to the homogeneous, anisotropic stress. It is assumed that the materials are mixed with given volume fractions…
We consider uniformly strongly elliptic systems of the second order with bounded coefficients. First, sufficient conditions for the invariance of convex bodies obtained for linear systems without zero order term in bounded domains and…
We derive exact critical-temperature bounds for the classical ferromagnetic Ising model on two-dimensional periodic tessellations of the plane. For any such tessellation or lattice, the critical temperature is bounded from above by a…
Almost four decades ago, Bergman and Milton independently showed that the isotropic effective electric permittivity of a two-phase composite material with a given volume fraction is constrained to lie within lens-shaped regions in the…
A liquid can exist under conditions of thermodynamic stability or metastability within boundaries defined by the liquid-gas spinodal and the glass transition line. The relationship between these boundaries has been investigated previously…
Elastic properties of the solid regions of neutron star crusts and white dwarfs play an important role in theories of stellar oscillations. Matter in compact stars is presumably polycrystalline and, since the elastic properties of single…
Motivated by the existing complications of finding solutions of Eringen nonlocal model, an alternative model is developed here. The new formulation of the nonlocal elasticity is centered upon expressing the dynamic equilibrium requirements…
Non-Euclidean plates are a subset of the class of elastic bodies having no stress-free configuration. Such bodies exhibit residual stress when relaxed from all external constraints, and may assume complicated equilibrium shapes even in the…
We derive expressions for classical isothermal and adiabatic elastic constants for periodic systems with the boundary contributions included explicitly. The potential-dependent part of these expressions is written in terms of potential…
The isotropic elastic moduli closest to a given anisotropic elasticity tensor are defined using three definitions of elastic distance, the standard Frobenius (Euclidean) norm, the Riemannian distance for tensors, and the log-Euclidean norm.…