Stress-based estimates and bounds of effective elastic properties: The case of cracked media with unilateral effects

Luc Dormieux (1) , Djimedo Kondo (2)

1 navier umr 8205 - Laboratoire Navier
2 LML - Laboratoire de Mécanique de Lille - FRE 3723

For direct insight into the stress concentration rule, stress-based boundary conditions are most appropriate. In this framework, the dilute and Mori–Tanaka estimates are shown to be identical for frictionless closed cracks. This extends a result already known for of opened cracks. The link with strain-based homogenization is also provided. In order to take into account the effects of the spatial distribution of cracks, a stress-based lower bound of the effective compliance dual of the strain-based upper bound of the stiffness proposed in [9] is derived. Illustrations for parallel closed cracks are presented.

Mots clés: Homogenization; Micromechanics; Cracking; Anisotropy; Eshelby tensor; Unilateral effects

Luc Dormieux, Djimedo Kondo. Stress-based estimates and bounds of effective elastic properties: The case of cracked media with unilateral effects. Computational Materials Science, 2009, 46 (1), pp.173-179. ⟨10.1016/j.commatsci.2009.02.027⟩. ⟨hal-00395195⟩