TABLE OF CONTENTS Our aim in this chapter is to study in more detail the equations of linear elasticity as well as the boundary conditions that are associated with them.
Throughout Part 3 of this book, we change our notations and call x the Lagrangian variable and x ? the Eulerian variable. Hence, x ? = ?( x, t) = x + u( x, t) represents the position at time t > 0 of the particle occupying the position x at time 0, u( x, t) denoting the displacement of this particle.
We recall that for an elastic material, and under the small deformations assumption, the stress strain law, which is linear, is
where ? ij = 1/2( u i,j + u j,i), u being the displacement and u i,j = ? u i/ ? x j denoting the derivative of u i with respect to the (Lagrangian) variable x j.
The quantities ? and are the Lam coefficients of the material, and the second principle of thermodynamics implies...
