SUMMARYWe present a meso-scale model for failure of heterogeneous quasi-brittle materials. The model problem of heterogeneous materials that is addressed in detail is based on two-phase 3D representation of reinforced heterogeneous materials, such as concrete, where the inclusions are melt within the matrix. The quasibrittle failure mechanisms are described by the spatial truss representation, which is defined by the chosen Voronoi mesh. In order to explicitly incorporate heterogeneities with no need to change this mesh, some bar elements are cut by the phase-interface and must be split into two parts. Any such element is enhanced using both weak and strong discontinuities, based upon the Incompatible Mode Method. Furthermore, a dedicated operator split solution procedure is proposed to keep local any additional computation on elements with embedded discontinuities. The results for several numerical simulations are presented to illustrate the capabilities of the proposed model to provide an excellent representation of failure mechanisms for any different macroscopic loading path.

International audienceThis paper presents a Finite Element model for the modeling of the failure of heterogeneous material at the meso-scale. This model is cast into the framework of the Enhanced Finite Element Method (E-FEM). Two kinds of enhancement are performed: (1) in the displace-ment field (strong discontinuity approach) in order to take into account micro-cracks, (2) in the strain field (weak discontinuity) in order to take into account heterogeneities without any mesh adaptation. Mechanical applications (uniaxial tension and compression loading, non-proportional loading) are performed in the context of cementitious materials such as concrete. We show the capability of the model to represent some of the main features of such materials observed at macro-scale