Interaction, in real time, between a designer and a virtual prototype is a promising way to optimize the parts design in mechanical industries. These interactions can induce deformation of some flexible parts of the prototype. The analysis in real time of nonlinear mechanical model by finite element method (FEM) is impossible. Our approach is based on two phases: 1-some load cases, characteristic of possible handlings, are precalculated; 2-results of this campaign are interpolated during the real-time immersion. This paper compares 4 approaches to calculate a reduced result of the campaign as fast as possible: an a posteriori reduction, an a priori enrichment method, an a priori enrichment-reduction and the hyperreduction.

Discrete element method (DEM) is an interesting alternative to classical approaches as the finite element method (FEM) to simulate homogeneous and heterogeneous materials. Indeed, although DEM was initially developed to simulate granular systems in motion, it also enables to model a continuous medium with the help of a dense granular packing in which the cohesion is introduced between each pair of particles in contact using beam or spring elements. However, among other issues, the local stress field obtained using DEM is heterogeneous, even in the case where it is theoretically homogeneous. In the present contribution, we investigate the stress field distribution in 3D DEM mechanical simulation, and propose an approach we named Halo, to evaluate the level of stress distribution. The idea of the method is to evaluate the stress at the scale of every discrete element (DE) taking into account the contribution of its neighbors, inside the Halo of the DE. The effect of the number of DEs per Halo on the stress distribution is discussed in homogeneous and heterogeneous media. The approach results for homogeneous media are compared to FEM calculations and to the theoretical Hertz solution via a Brazilian test. For the homogeneous media, we use the unidirectional flax/bio based epoxy composite, for which macroscopic longitudinal Young’s modulus is experimentally quantified. Furthermore, comparisons with FEM are performed in this context. Results highlight a good agreement between both approaches in terms of stress fields including extremal values.

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