Asymptotic analysis of an elastic thin interphase with mismatch strain

Raffaella Rizzoni (1) , Frédéric Lebon (2)

1 Dipartimento di Ingegneria
2 M&S - Matériaux et Structures

This paper proposes the study of the equilibrium problem, where two elastic bodies are bonded to a thinelastic film under mismatchstrain conditions resulting in a state of residual stress. The asymptotic behavior of the film/adherent system is modeled as the film thickness tends to zero, using a method based on asymptotic expansions and energy minimization procedures. This method yields a family of non-local imperfect interface laws, which define a jump in the displacement and the traction vector fields. The amplitudes of the jumps turn out to be correlated with the state of residual stress and the elastic properties of the materials. As an example, the interface law is calculated at order zero in the case of a pure homogeneous mismatchstrain and a thin isotropic film consisting of Blatz-Ko material.

Mots clés: Thin interphase; Mismatch strain; Composite material; Contact law

Domaines: Mécanique des solides [physics.class-ph]; Mécanique des solides [physics.class-ph]

Raffaella Rizzoni, Frédéric Lebon. Asymptotic analysis of an elastic thin interphase with mismatch strain. European Journal of Mechanics - A/Solids, 2012, 36, pp.1-8. ⟨10.1016/j.euromechsol.2012.02.005⟩. ⟨hal-00694059⟩