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摘要
In order to consider the effects of nonuniform mesoscopic(local) stress field and strain field on the macroscopic mechanical response of porous rock under loading, a multi-scale elastoplastic constitutive model based on incremental variational theory was established. Firstly，the porous rock was assumed to be a composite material composed of a pressure-sensitive solid matrix and spherical pores. In this context，the incremental variational principle for porous rock was proposed. Secondly，the local mechanical behaviors of solid matrix were assumed to obey a threshold and isotropic hardening parabolic Mises-Schleicher plastic model, the local increment potential of solid matrix as well as the effective incremental potential of porous rock were deduced. The macroscopic stress-strain relationship of porous rock was obtained by optimizing the effective incremental potential and combining with the Mori-Tanaka homogenization method. Finally，a numerical algorithm for the multi-scale elastoplastic constitutive model was developed based on the traditional return mapping algorithm，and a UMAT subroutine was compiled to embed the multi-scale model into Abaqus software. The accuracy and effectiveness of the multi-scale model were verified by comparing the simulation results of the multi-scale model with the finite element unit cell model(reference solutions) as well as the test data of typical Vosges sandstone. The results show that the numerical solution of the multi-scale model based on the incremental variational theory was in a good agreement with the finite element reference solution，and can accurately reproduce the macroscopic mechanical behavior of the Vosges sandstone. ? 2022 Academia Sinica.
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