An anisotropic gradient damage model based on microplane theory

In this paper, a thermodynamically consistent formulation and numerical implementation of a gradient-enhanced anisotropic microplane damage model are proposed. The microplane model is derived based on the volumetric-deviatoric split and the kinematic constraint assumption. The mixed finite element formulation of displacement and nonlocal strains field is developed to simulate anisotropic quasi-brittle fracture. The proposed model is used to describe the mechanical behavior of anisotropic quasi-brittle materials by numerical simulations of uniaxial tension, simple shear, tension of a bar with localized deformation, and a rectangular specimen with a material imperfection. The results show the ability of the proposed approach to predict mesh-independent results for quasi-brittle damage behavior accompanied by the localization of deformation. Comparison between numerical and experimental results shows that the relatively simple model based on microplane theory together with the standard finite elements implementation is capable to realistically simulate complex behaviors related to fracture of quasi-brittle material such as concrete.