Abstract
The skin is made of three main layers which are, from the top to the bottom: the epidermis, the dermis and the hypodermis. We consider the dermis as made of a Stokes fluid interacting with a periodic network of elastic fibers, assumed to obey the linearized elasticity law of behaviour. Above and below, the epidermis and the hypodermis are elastic solids. As the dimension of the thickness is very small compared to the two others, we assume periodic boundary conditions in those two planar directions. We study the 3d fluid–structure interaction system in a first part, and in a second part, we make the characteric size of the periodic element of the network go to zero in order to find an homogenized law for the whole skin. Starting from linear elastic materials, we find a viscoelastic law at the limit.