Coupled continuous–discrete formulation based on microplane and strong discontinuity models for representing non-orthogonal intersecting cracks

Abstract Fracture process in quasi-brittle materials is governed by the strain localization phenomenon which involves the formation of localized damage zones and cohesive cracks. In this work, we present numerical tools to model strain localization from the onset of localized damage to the formation and propagation of multiple intersecting cracks. Two main ingredients are used for this purpose: (i) a microplane model, to describe the initial anisotropic damage phase; (ii) the strong discontinuity method, to introduce cracks as strong discontinuities in the damaged continuum using the Embedded Finite Element Method (E-FEM). Here, we formulate the microplane microdamage model in a thermodynamic framework using simple constitutive laws on each microplane. In order to describe multiple intersecting cracks, we extend the standard E-FEM to accommodate two strong discontinuities. The coupling between microplane microdamage model with the strong discontinuity model is achieved using a transition method based on the energy equivalence between both models. Exploiting the anisotropic description provided by the microplane model, transition criteria are formulated based on the quantities defined on each microplane. The proposed methodologies are illustrated using several elementary test cases that involve both simple and complex stress–strain states.