Regularization of microplane damage models using an implicit gradient enhancement

Abstract

The microplane model allows for the description of damage induced anisotropy in a natural manner by introducing constitutive laws for quantities on individual microplanes at each material point. However, if damage or other strain softening constitutive laws are used within the microplane approach, the well-known problem of localization arises leading to spurious results and mesh dependency. This problem demands some regularization method to stabilize the solution. The paper focuses on the efficient implementation of implicit gradient enhancement for microplane damage models. Previous works enhanced the strain tensor, thus resulting in large number of extra degrees of freedom, which limits the use of this method for large scale 3D simulations. A new method which enhances the equivalent strain driving the damage on each microplane is introduced in this work. The new method limits the number of additional degrees of freedom to one, while preserving the regularizing effect. The two methods are implemented within a 3D finite element code to compare their performance. The microplane model used is based on a thermodynamically consistent formulation and on a volumetric–deviatoric split of strains on each microplane. Furthermore, an exponential damage law is used and an equivalent strain expression which distinguishes between compression and tension is applied to simulate the behavior of concrete. The capabilities of the proposed formulation are demonstrated by comparison to published experiments on plain concrete.