The concept of internal constraints is extended to gradient materials. Here,
interesting constraints can be introduced, such as pseudorigid ones. The stresses and
the hyperstresses will be given by constitutive equations only up to reactive
parts, which do no work during any compatible motion of the body. For
the inclusion of thermodynamical effects, the theory is generalized to the
case of thermomechanical constraints. Here one obtains reactive parts of
the stresses, heat flux, entropy, and energy, which do not contribute to the
dissipation. Some critical remarks on the classical concept of internal constraints
are finally given. A method to introduce internal constraints in a natural
way is described to overcome some conceptual deficiencies of the classical
concept.