A smooth Crack-Band Model for anisotropic materials: Continuum theory and computations with the RKPM meshfree method

Abstract

A smooth Crack Band Model (sCBM) is developed for anisotropic materials with both high and low magnitude of anisotropy. sCBM is primarily used as a regularization mechanism to enable capturing the correct size and shape of the fracture process zone (FPZ) as well as the smooth distribution of strain inside the zone. The versatility of the proposed sCBM formulation is demonstrated by its adaptability to any material law of choice. A Reproducing Kernel Particle Method (RKPM) is employed to discretize such formulation, the benefit of which is its ability to compute the Hessian of the displacement field (i.e., the sprain tensor), a key quantity in the sCBM theory, using only the nodal displacements as the problem unknowns. This makes the resulting formulation accurate and efficient, which is shown by the validations against size-effect and radial crushing experiments, illustrating the power of the proposed methodology for practical applications.