Rate-dependent non-viscous potential stress (Q2548469)

In the context of variational continuum mechanics this paper considers stresses analogous to Lorentz and Coriolis forces, that is to say stresses which are rate dependent but which are non-dissipative (er non-viscous). A dynamical potential is constructed so that an application of Hamilton's principle to a Lagrangian leads to stresses of this type. The requirements of material objectivity are satisfied and the material is assumed to be isotropic. The contributions of such stresses to the energy and momentum are constructed. In a small strain example the velocity dependent stresses introduce an interaction between transverse and longitudinal modes of vibration which would be energetically separate in the corresponding problem involving a linearly elastic material.