Brittle Anisotropy based on a Tensor Damage Phase Field Model

Abstract

A consistent model that properly captures the behavior of materials when submitted to loads and at the same time considers the influence of damage growth in the material properties is a challenging task. Specially in brittle materials, due to the mechanism of cleavage, as the damage grows, the material mechanical response is differently degraded according to the load direction considered, characterizing an anisotropic damage. A fourth-order degradation tensor is used with a phase field framework in order to model the induced damage anisotropy without the need of defining the damage principal direction a priori. The transient non-linear coupled system of equations is solved using appropriate time integration procedures. Due to the mild nonlinearities, standard linearization methods are not considered. The numerical examples illustrate the model's features and conclude that the adopted approach is able to simulate anisotropic damage totally driven by the strain state of the material.