Anisotropic damage of concrete: A three-dimensional approach with energy-based loading surfaces and a new evolution law

This paper presents a three-dimensional model to simulate the tensile behavior of concrete based on continuum damage mechanics. By using a symmetric second-order tensor as the damage variable, this model allows for the simulation of orthotropic degradation. Three decoupled loading functions are defined in quantities that are thermodynamically conjugate to the damage variables; the use of these specific definitions yields a symmetric tangent stiffness. In order to allow FE-calculations with arbitrary meshes, a process zone width is introduced in the damage evolution. A Newton-Raphson-Method is used to solve the resulting nonlinear system of equations, and all partial derivatives are presented. Finally, the evaluation of the model is carried out by means of standard experimentation.