On a class of non-linear elastic materials

This article deals with a family of non-linear hyperelastic materials M(epsilon) depending on a parameter epsilon varying from 0 to 1; M(0) is a masonry-like material and M(1) is linear elastic. Some properties of the function (T) over cap (E; epsilon) delivering the Cauchy stress corresponding to the infinitesimal strain E, are proved; in particular, it is shown that T(E; E) is strongly monotone for epsilon > 0 and monotone for epsilon = 0. Moreover, denoting by [u(.;epsilon), E(.;epsilon): T(.;epsilon)] the solution to the equilibrium problem for solids made of a material M(epsilon), the convergence of [u(.;epsilon): E(.;epsilon), T(.;epsilon)] for epsilon going to 0 and 1, is investigated. (C) 2000 Elsevier Science Ltd. All rights reserved.