On The Geodesic Property Of Strain Field Patterns In Elastoplastic Composites

Dominique Jeulin (1) , Wei Li (2) , Martin Ostoja-Starzewski (3)

1 CMM - Centre de Morphologie Mathématique
2 Department of Mechanical Engineering [Montréal]
3 Department of Mechanical Science and Engineering [Urbana]

Under study is the geodesic (i.e. shortest path) character of strain fields occurring in inelastic response of matrix-inclusion composites. The spatially random morphology of composites is created by generating the inclusions centres through a sequential inhibition process based on a planar Poisson point field preventing any disc overlaps. Both phases (inclusions and matrix) are elastic-plastic hardening with the matrix being more compliant and weaker than the inclusions, and perfect bonding holding everywhere, so that the plastic flow occurs between the inclusions. A quantitative comparison of a response pattern obtained by computational mechanics with that found only by mathematical morphology indicates that (i) the regions of plastic flow are close (or even very close) to geodesics and (ii) a purely geometric (and orders of magnitude more rapid than by computational mechanics) assessment of these regions is possible.

Mots clés: geodesics; elastoplasticity; random composites

Domaines: Equations aux dérivées partielles [math.AP]

Dominique Jeulin, Wei Li, Martin Ostoja-Starzewski. On The Geodesic Property Of Strain Field Patterns In Elastoplastic Composites. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2008, 464 (2093), pp.1217-1227. ⟨10.1098/rspa.2007.0192⟩. ⟨hal-00830724⟩