Mechanics of continuous media with interfaces

Abstract

The basis for the description of the mechanical properties of materials is the definition of a model representing the characteristic properties of real materials. The first step in the analysis of the properties of any mechanical system is the definition of its geometrical model — in the case of materials a structural model.

For the purposes of describing their structure, materials can be divided into two groups, namely simple, with one physical (atomic or molecular) level of structure, and complex, with the structure on a level of particles, continuous or discontinuous phases. The theory of physical structures, crystallography, is based on point models of simple solid materials. The theory of structures consisting of particles lacks a universal structural model; their structural parameters are defined and measured by stereology.

This paper is concerned with a model of non-homogeneous materials with interfaces, i.e. with a granular structure. It derives quantities describing materials with volume and surface inhomogeneities and shows the procedure for deriving the equations of continuum mechanics for such materials.