A Gradient Enhancement with Application to Anisotropic Continuum Damage

Abstract.The paper focuses on the modelling of the quasi-brittle failure of materials with a heterogeneous microstructure. Failure induced anisotropy is incorporated in terms of the microplane theory. This theory is based on scalar damage laws formulated on several individual material planes. Anisotropy of the overall constitutive law is introduced in a natural fashion by transforming the scalar valued damage operators into a damage tensor of fourth order. To account for microstructural interaction, strain gradients are included in the constitutive equations to preserve the well-posedness of the underlying boundary value problem in the postcritical regime. The gradient enhancement of the continuum model results in an additional partial differential equation defining an averaged quantity, the nonlocal strain tensor. This additional gradient equation is satisfied in a weak sense which leads to a modified finite element formulation with the nonlocal strains as additional nodal degrees of freedom. The governing equations are linearized consistently and solved within an incremental iterative Newton Raphson solution procedure. The gradient enhanced finite element formulation for anisotropic damage will be illustrated by means of several numerical examples.