We present an atomic scale theory of lattice distortions using strain-related variables and their constraint equations. Our approach connects constrained atomic length scale variations to continuum elasticity and describes elasticity at several length scales. We apply the approach to a two-dimensional square lattice with a monatomic basis and find the elastic deformations and hierarchical atomi...

The singularities that we consider are the characteristic non-smooth solutions of the equations of linear elasticity in piecewise homogeneous media near two dimensional corners or three dimensional edges. We describe here a method to compute their singularity exponents and the associated angular singular functions. We present the implementation of this method in a program whose input data are g...

In this paper we study the global unique continuation property for the elasticity system and the general second order elliptic system in two dimensions. For the isotropic and the anisotropic systems with measurable coefficients, under certain conditions on coefficients, we show that the global unique continuation property holds. On the other hand, for the anisotropic system, if the coefficients...

In this note we develop tools and techniques for the treatment of anisotropic thermo-elasticity in two space dimensions. We use a diagonalisation technique to obtain properties of the characteristic roots of the full symbol of the system in order to prove L–L decay rates for its solutions.

The writer’s theory of surface instability of au elastic body under initial stress in finite strain is extended to anisotropic elasticity. The general characteristic equation for surface instability is derived. In addition, the surface deflexion under a normal load is evaluated for the subcritical case of initial stress. The analysis includes the case in which gravity is taken into account. It ...

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 method of treatment is sketched and for the cases of cubic media and hexagonal media detailed studies are provided.

We comment on the new trend in mathematical physics that consists of obtaining Taylor series for fabricated linear and nonlinear unphysical models by means of homotopy perturbation method (HPM), homotopy analysis method (HAM) and Adomian decomposition method (ADM). As an illustrative example we choose a recent application of the HPM to a dynamic system of anisotropic elasticity.

Every linear planar anisotropic elastic material is equivalent, under a linear change of coordinates, to an orthotropic material. Consequently, up to linear changes of variables, there are just two "canonical" planar elastic moduli which determine the properties of any linearly elastic material. Extensions to three-dimensional elasticity and applications are indicated.