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La Morpho-Math au CDM

Séminaire du Centre des Matériaux

Le Centre des Matériaux accueillera le 12 septembre 2016 à 14h en C001, deux chercheurs du Centre de Morphologie Mathématique (CMM) de MINES ParisTech, situé à Fontainebleau.

François WILLOT, chercheur au CMM présentera "The behavior of the effective yield stress in 2D perfectly-plastic, porous random media"

Abstract : A broad range of physical phenomena in material science involve the emergence of surfaces or paths of minimal energy. Examples include domain walls in random Ising systems (Huse et al, 1985), current localization in varistors (or non-Newtonian fluid flow) (Donev et al, 2001), the onset of voltage in polycrystals (Haslinger et al, 2000), or ductile fracture (De Arcangelis et al, 1989; Bouchaud et al, 1993).
In this work, we examine the connection between the “shortest-path” and “minimum-cut” problems (Duxbury et al, 2006) and the strain field localization patterns occuring in 2D porous media. Rigid perfectly-plastic media are considered and their response determined using Fourier methods. The length of the geodesics (i.e. shortest paths) in 2D random media is computed analytically and numerically, in
the limit of a vanishingly small porosity. These results are used to interpret the behavior of the effective yield stress in terms of the length of geodesics.

Jean-Baptiste Gasnier, doctorant au CMM, présentera son travail de thèse intitulé "The influence of cracks on the thermoelastic response of a TATB-based polycrystal"

Abstract : We present a combined numerical and experimental study of the thermoelastic response of polycrystalline TATB. The numerical implementation relies on a parametrized tesselation of space yielding non-convex, prolate grains and providing realistic granulometry curves for the polycrystaline microstructure (Gasnier et al, Mat ́eriaux & Techniques, 2015). Various populations of inter and transgranular micro-cracks are incorporated in the model, in an effort to account for the variations of the volumetric expansion coefficient under thermal cycles, during cooling and heating. The cracks orientation are either correlated or uncorrelated to the symmetry planes of the local crystal. Specifically, we consider transgran- ular cracks that are placed along the “weakest” or “stiffest plane” of the TATB crystal. The macroscopic, and full-field responses, of the cracked polycrystal models are predicted using Fourier-based numerical computations on voxel grids. Numerical results demonstrate that the decrease of the thermal expansion coefficient during cooling cycles is consistant with transgranular cracking along weakest planes, and not with other transgranular, or intergranular cracks. An analytical homogenization procedure that takes into account the anisotropy of the TATB crystal is proposed to interpret this result. This is in contrast with thermal cycle data during heating, which is reproduced by intergranular cracking. Additionaly, it is found that cracks closing and opening account for the variations of the tangent elastic moduli observed during compression cycles.

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