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

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