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

V.A. Levin1, I.I. Vdodichenko1, A.V. Vershinin1, M.Y. Yakovlev2, K.M. Zingerman3,4
1Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Russia, 119991, Moscow, 1 Leninskiye Gory, Main Building
2Fidesys LLC, Office 402, 1 bld. 77, MSU Science Park, Leninskie Gory, Moscow 119234
3Tver State University, 170100, Russia, Tver, 33, Zhelyabov st.
4National Research Nuclear University MEPhI. 115409, Russia, Moscow, Kashirskoe shosse, 31


The set of points of strength surface in the space of principal stresses is determined for 2D case. The approximation of this set of points permits one to obtain the strength criterion in the analytical form.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. The representative area of the material is specified. The representative area contains pores. 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. The 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 computed. The principal values of stresses at which fracture occurs are computed. By this way, a point on a plane of principal stresses is determined; this point corresponds to the specified boundary-value 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 permits one to obtain a macroscopic strength criterion in 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.

Received: 21 September 2017   Revised: 28 October 2017   Accepted: 31 October 2017

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