María Teresa Cao-Rial

In this paper, we consider a family of linearly elastic shells in normal compliance contact with a deformable foundation. We obtain error estimates for the approximation of the solution to a three-dimensional (3D) problem with a two-dimensional (2D) limit solution in terms of the thickness ε of the shell. The proof of the main result relies on a corrector method. We also provide a strong formulation for the 2D obstacle boundary value problem associated.

This work aims to derive an expression for the energy release rate for hyperelastic materials using the configurational force framework. As a specific example, the classical expression of the path-independent J-integral for elastic materials undergoing small deformations will be derived.

Models involving interfaces with discontinuities or even singularities of some fieldsacross them are very frequent in real life problems modelling. The use of the eXtendedFinite Element Method (XFEM) instead of the traditional FEM has two advantages: themesh of the domain can be independent of the interface position, and it allows toenrich an area with specific shape functions fitted to singularities of the expectedsolution. Nevertheless, a critical point of its implementation is the different kind (andnumber) of degrees of freedom on each node. In this paper we present a detaileddescription of XFEM implementation, with special emphasis on the terms that involveintegration over interfaces. The methodology is presented in a general context, and asan example, we will apply it to a problem of solids mechanics. In particular, we willcontextualize the procedure on a Rayleigh waves propagation problem in a crackedstructure considering a Signorini contact condition on the crack sides.

In this paper we consider a family of three-dimensional problems in thermoelasticity for linear elliptic membrane shells and study the asymptotic behaviour of the solution when the thickness tends to zero.We fully characterize with strong convergence results the limit as the unique solution of a two-dimensional problem, where the reference domain is the common middle surface of the family of three-dimensional shells. The problems are dynamic and the constitutive thermoelastic law is given by the Duhamel-Neumann relation.