Anisotropic nonlocal damage model for materials with intrinsic transverse isotropy

This paper presents the theoretical formulation and numerical implementation of an anisotropic damage model for materials with intrinsic transverse isotropy. Crack initiation and propagation are modeled by phenomenological damage evolution laws, controlled by four equivalent strain measures. The latter are constructed so as to distinguish the mechanical response of the material in tension and compression, along the direction perpendicular to the bedding plane and within the bedding plane. To avoid mesh dependency induced by softening, equivalent strains are replaced by nonlocal counterparts, defined as weighted averages over a neighborhood scaled by two internal length parameters. Finite Element equations are solved with a normal plane arc length control algorithm, which allows passing limit points in case of snap back or snap through. The model is calibrated against triaxial compression tests performed on shale, for different confinements and loading orientations relative to the bedding plane. Gauss point simulations confirm that the model successfully captures the variation of uniaxial tensile strength with respect to the bedding orientation. Finite Element simulations of three-point bending tests and compression splitting tests show that nonlocal enhancement indeed avoids mesh dependency, and that the axial and transverse dimensions of the damage process zone are scaled by the two characteristic lengths. Results further show that the damage process zone is direction dependent both in tension and compression. The model can be used for any type of textured brittle material; it allows representing several concurrent damage mechanisms in the macroscopic response and interpreting the failure mechanisms that control the damage process zone.