On a class of non-linear elastic materials

This article deals with a family of non-linear hyperelastic materials depending on a parameter varying from 0 to 1; is a masonry-like material and is linear elastic. Some properties of the function delivering the Cauchy stress corresponding to the infinitesimal strain E, are proved; in particular, it is shown that is strongly monotone for >0 and monotone for =0. Moreover, denoting by u(·;), E(·;), T(·;)] the solution to the equilibrium problem for solids made of a material the convergence of u(·;), E(·;), T(·;)] for going to 0 and 1, is investigated.