An approach to the computation of effective strength characteristics of porous materials

Abstract

An approach to the computation of effective strength characteristics of porous materials is developed. The approach is implemented for 2D problems (plane strain) within the scope of linear elasticity. The approach can be generalized for 3D problems and nonlinear elasticity. The specific features of the proposed approach are as follows. First, a representative area of material which contains pores is specified. A series of boundary-value problems is solved under periodical boundary conditions for different types of deformation of the external boundary. The finite element method is used for solution. Averaging of stresses is performed for each problem, and the principal values of averaged stresses are computed. The maximal value of the stress intensity over the representative area is then calculated. Finally, principal values of stresses at which fracture occurs are computed. By this way, a point on a plane of principal stresses is determined, which corresponds to the specified boundaryvalue problem. A set of such points is formed for the series of boundary-value problems, and the boundary points of this set are determined. The obtained set of boundary points is approximated by a polygonal line. The parameters of segments of this polygonal line are computed. This computation allows one to obtain a macroscopic strength criterion in an analytical form. The obtained relations can be further reduced to the form of the Mohr-Coulomb criterion. The numerical results are given in the paper for a particular case in which the representative area is a square containing a centered elliptical hole.