From continuous to discontinuous failure in a gradient-enhanced continuum damage model

A computational framework for the description of the combined continuous–discontinuous failure in a regularised strain-softening continuum is proposed. The continuum is regularised through the introduction of gradient terms into the constitutive equations. At the transition to discrete failure, the problem fields are enhanced through a discontinuous interpolation based on the partition of unity paradigm of finite-element shape functions. The inclusion of internal discontinuity surfaces, where boundary conditions are applied without modifications of the original finite-element mesh, avoids the unrealistic damage growth typical of this class of regularised continuum models. Combined models allow for the analysis of the entire failure process, from diffuse microcracking to localised macrocracks. The discretisation procedure is described in detail and numerical examples illustrate the performance of the combined continuous–discontinuous approach.