Adaptive resolution of localized damage in quasi-brittle materials

This paper presents an adaptive mesh refinement technique suitable for the resolution of highly localized damage in concrete and other quasi-brittle materials. The objectivity of the description of softening is ensured by using regularized material models based on the concept of nonlocal averaging, which is applied to isotropic and anisotropic damage formulations. The distributions of strain and internal variables produced by such regularized models are continuous, which facilitates the projection of information from one finite element mesh onto another. However, not all mapping algorithms for the transfer of internal variables preserve the basic characteristics of the localized process zone. The paper evaluates and compares three mapping algorithms, which are based on the closest-point transfer, least-squares projection, and shape-function projection. It also briefly comments on other important components of a complete adaptive strategy, i.e., on the error indicator, refinement rules, and mesh generator. The efficiency of the proposed strategy is illustrated by examples that treat straight as well as curved crack trajectories. The underlying material model is a nonlocal integral formulation of anisotropic damage based on the microplane concept.