Damage and plastic friction in initially anisotropic quasi brittle materials

• A micro-mechanical model is proposed for coupled damage and plastic frictional sliding.
• The physical mechanism of plastic deformation due to frictional sliding of micro-cracks is considered.
• Initially inherent anisotropy is taken into account.
• A numerical method is proposed for Hill's tensor calculation in anisotropic materials.
• The efficiency of the proposed model is verified through numerical assessments and experimental comparisons.

A three dimensional micro-mechanical model is developed for modeling micro-crack growth and plastic frictional sliding in initially anisotropic quasi brittle materials under compressive loading. Macroscopic strains are attributed to elastic deformation of matrix and displacement discontinuity on micro-cracks. Effective elastic properties of cracked materials are determined using a Eshelby's solution based linear homogenization technique by considering micro-cracks as spheroidal inclusions. An efficient numerical method is used to calculate Hill polarization tensor for spheroidal micro-cracks arbitrarily embedded in transversely isotropic solid matrix. Based on this, the plastic strain related to frictional sliding on closed micro-cracks is determined by combining irreversible thermodynamics and homogenization method. A specific plastic friction criterion is formulated in terms of the local stress field on crack surfaces. The presence of a back stress tensor allows description of material hardening and softening without any additional functions. A specific damage evolution law is finally proposed. The evolutions of the friction-related plastic strain and crack-propagation induced damage are inherently coupled. A series of numerical assessments are presented for various loading paths such as uniaxial compression, triaxial compression and shear. The obtained numerical results clearly reveal that the macroscopic behaviors of cracked materials are strongly affected by the initial anisotropy. Finally, the performance of the proposed micro-mechanical model is verified by comparing numerical results and experimental data for a typical rock-like materials, shale.