A Generalized Interface Law in Dynamic Coupled Thermoelasticity: Asymptotic Analysis and Fem Validation
Résumé
The present work deals with the modeling of interfaces in coupled thermoelasticity by means of
the asymptotic analysis (see, e.g., [1, 2, 3]). The composite body is constituted by two thermoelastic media (adherents) bonded together by a thin intermediate thermoelastic layer (adhesive).
By considering a small parameter ε, associated with the thickness of the adhesive, we apply
the asymptotic expansions method to the thermoelastic evolution problem by letting ε tends to
zero. We characterize different limit interface laws, considering also the contribution of the
higher order terms of the expansion. The cases of soft (lowly-conduting) and hard (moderately
conducting) interfaces are considered: the first is derived assuming the constitutive coefficients
linearly depending on the thickness ε; the second considers the material properties independent
of ε. By using the approach developed in [4] for multiphysic materials, we also identify a general thermoelastic interface law which comprises the above aforementioned models. Numerical
investigations are performed in the framework of the finite element method, by comparing the
results obtained by modeling the adhesive as a continuum material (discretized in finite elements
even in the thickness) with the results carried out using the derived interface models.
