Numerical analysis of two non-linear soft thin layers

International audienceIn a first part, we consider a bar with extremities subject to a given displacement and made by two elastic bodies with linear stress-strain relation separated by an adhesive layer of thickness $h$. The material of the adhesive is characterized by a non convex (piecewise quadratic) strain energy density with elastic modulus $k$. After considering the equilibrium problem of the bar and determining the stable and metastable solutions, we let $(h,k)$ tending to zero and we obtain the corresponding asymptotic contact laws, linking the stress to the jump of the displacement at the adhesive interface. The second part of the paper is devoted to the bi-dimensional problem of two elastic bodies separated by a thin soft adhesive. The behaviour of the adhesive is non associated elastic-plastic. As in the first part, we study the asymptotic contact laws