Homogenized Interface Model Describing Inhomogeneities Located on a Surface

Martin David (1) , Catherine Pideri (2) , Jean-Jacques Marigo (3)

1 LAMSID - UMR 8193 - Laboratoire de Mécanique des Structures Industrielles Durables
2 IMATH - Institut de Mathématiques de Toulon - EA 2134
3 LMS - Laboratoire de mécanique des solides

We study the influence of heterogeneities located near a planar surface on the elastic response of a three-dimensional elastic medium. These heterogeneities can be either reinforcements, like steel reinforce- ments in concrete, or defects, like micro-cracks periodically distributed. We prove that their influence is of the second order from an energetic viewpoint. Then, we propose an "up to second order effective model" in which the influence of the heterogeneities is given by a surface energy contribution involving both the jump of displacement across the surface and the tangential strain components on the surface. The effective coefficients entering in the definition of the surface energy are obtained by solving "elementary" elastic problems formulated on an infinite representative cell containing the defects. We analyze this model, in particular the properties of the effective surface coefficients, and establish its coherence with limit models previously described in the literature for stiff or soft interfaces. This approach is finally applied to several kinds of heterogeneities.

Domaines: Mécanique [physics.med-ph]

Martin David, Catherine Pideri, Jean-Jacques Marigo. Homogenized Interface Model Describing Inhomogeneities Located on a Surface. Journal of Elasticity, 2012, 109 (2), pp.153--187. ⟨10.1007/s10659-012-9382-5⟩. ⟨hal-00655496⟩