On hyperelasticity with internal constraints

By requiring the constitutive equation for the specific internal energy to be such that energy is balanced for all motions compatible with the internal constraint, we are able to infer the existence and the direction of the reactive stress as well as the usual stress relation for the active stress. In contrast with previous work along this line, our analysis avoids the Lagrange multiplier formalism, and we need not assume that the internal energy response function is extendable off the constraint manifold.