A new incremental variational micro-mechanical model for porous rocks with a pressure-dependent and compression–tension asymmetric plastic solid matrix

Abstract

In this paper, we shall formulate a new micro-mechanical model for describing both local and macroscopic elastic–plastic behavior of porous rocks with a pressure-sensitive and tension–compression asymmetric solid matrix. For this purpose, a new incremental variational mean field homogenization (IVMFH) method is first established. The novelty lies in the fact that the new formulation allows considering solid matrix obeying a nonlinear plastic yield criterion rather than the linear Drucker–Prager one adopted in the previous work Zhao et al. (2019). To this end, a new optimization procedure is proposed to estimate the effective incremental potential involving a stress-dependent relation between volumetric and deviatoric parts of local plastic strain field of solid matrix. The proposed incremental variational model takes into account the effect of non-uniform distribution of local stress and strain fields in solid matrix by incorporating their first and second moments in the homogenization process. The proposed model is able to provide not only macroscopic but also local mechanical responses of porous rocks. Its efficiency is assessed by a series of comparisons with full-field finite element calculations. Application examples are also presented through comparisons with experimental data for two typical porous rocks: Vosges sandstone and Lixhe chalk.