The linear theory of second-grade elastic materials
Second-grade elastic materials have an energy density which depends on both first and second deformation gradients. The behaviour of these materials is investigated for deformations sufficiently small that the equations of motion can be linearized. The elastic materials with couple stress studied by Mindlin and Tiersten [1] are a special case of the materials studied here, and our results reduce to theirs with an appropriate choice for our elastic constants.