The contribution is dedicated to the mechanical simulation of heterogeneous media using a cohesive discrete element method. This latter uses an equivalent continuous model based on granular packings typically composed of disks in 2D and spheres in 3D. In the present work, granular packings are generated using the efficient Lubachevsky-Stillinger algorithm and the cohesion between particles is modeled using beam elements described by Euler-Bernoulli theory. In such an approach, the local parameters related to the geometry and the mechanical behavior of the beam element does not fit the macroscopic elastic coefficients. As a result, a calibration process is set up to relate local and macroscopic parameters. Please notice that only two local parameters, namely the microscopic Young's modulus and the dimensionless thickness of the beam suffice to characterize the elastic behavior of an isotropic medium. Similarly to a finite element method, the issue of discretization is of crucial importance since this directly affects the accuracy of results. That is why, we perform preliminary tests to estimate the suitable number of particles using the discrete element code MULTICOR3D developed in our laboratory. In the context of a homogeneous medium, it turns out that a minimum number of particles of 700,000 particles has to be considered to avoid discretization effects.

In a first step, several tests are carried out on 2D and 3D models composed of a single inclusion or a more complex microstructure composed of several spherical or circular inclusions. Comparisons are done with several numerical approaches such as the finite element and the fast-Fourier based methods. These highlight the ability of the proposed DE approach to yield a suitable elastic response in the context of heterogeneous media. In a second step, interfacial debonding and a failure criterion based on the hydrostatic stress are considered. The idea is to better appreciate the
suitability of the discrete element method to model cracks initiation and propagation in heterogeneous media. Again, results exhibit the consistency of this approach in comparison with the finite element one. These findings are encouraging and enable us to expect thermomechanical simulations in a next future.