Asymptotic development for bonded composite elastic structures: Gamma-limit and analytical examples

The paper analizes in a one-dimensional setting the asymptotic behavior of a composite elastic bar constituted of two adherent parts separated by a thin adhesive layer of small thickness. The energy densities of the adhesive and the adherents and are assumed to be quadratic with different elastic moduli. The expansion of the energy functional is studied as the adhesive thickness goes to zero but keeping the adherents' moduli fixed. The analysis, relying upon Gamma-convergence techniques, shows that at order one the glue behaves like a line segment across which displacements and stresses undergo jump discontinuities. discontinuities.