Effects of inclusions and pores on plastic and viscoplastic deformation of rock-like materials

The aim of this paper is to study effects of inclusion and pores on plastic and viscoplastic deformation of rock-like materials. We shall consider a class of clayey rocks with two separate scales of microstructure. At the mesoscopic scale, the material is constituted by a continuous matrix and embedded mineral inclusion. At the microscopic scale, the continuous matrix is a porous medium composed of a solid phase and spherical pores. Macroscopic deformation behavior of the material is determined by using a two-step homogenization procedure. An analytical plastic yield criterion is used for the porous matrix in the first step. It is assumed that the porous matrix exhibits both instantaneous plastic deformation and delayed viscoplastic deformation, which are described by a unified formulation. The plastic criterion is extended to serve as the viscoplastic loading function. At the mesoscopic scale, we shall investigate influences of inclusion stiffness, shape, orientation and volume fraction on plastic and viscoplastic deformation. Due to the absence of analytical solutions, we shall propose an extended Fast Fourier Transform method (FFT) to solve the nonlinear homogenization problem of the unit cell exhibiting time-dependent plastic deformation. A series of numerical simulations are performed and the obtained results show that the proposed numerical model is able to bring a finer description of complex microstructure effect than most analytical models. Finally, the efficacy of this numerical model is checked through comparisons between numerical results and experimental data in triaxial compression creep and relaxation tests on claystone.