Nonlocal enrichment of a micromechanical damage model with tensile softening: advantages and limitations
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Upon crack propagation, brittle geomaterials such as concrete and rock exhibit a nonlinear stress/strain behavior, damage induced stiffness anisotropy, loading path dependent strain softening and hardening, unilateral effects due to crack closure and a brittle-ductile transition, which depends on the confining pressure. Challenges in theoretical and numerical modeling include the distinction between tensile and compressive fracture propagation modes, mesh dependency during softening, and lack of convergence when several critical points are expected on the stress/strain curve. To overcome these issues, we formulate a nonlocal micromechanics based anisotropic damage model. A dilute homogenization scheme is adopted for calculating the deformation energy of the Representative Elementary Volume due to the displacement jumps at open and closed micro-cracks. Tension (respectively compression) damage criteria are expressed in terms of non-local equivalent strains defined in terms of positive principal strains (respectively deviatoric strains). Constitutive parameters are calibrated against published experimental data for concrete and shale. We employ the arc-length control method to solve boundary-value problems with the finite element package OOFEM: the algorithm allows capturing softening, snap back and snap through. We simulate the development of the compression damage zone around a cavity under biaxial far field stress conditions and the softening behavior consequent to tensile fracture propagation during a three-point bending test. No mesh dependency is noted during softening as long as micro-cracks do not interact.