Reduced Constraint Manifolds

The formalization of the concept of internal constraint is usually done by means of restrictions on the deformation gradients, by imposing that they must stay on a submanifold of Lin⁺. Our point of view is to impose restrictions on the right Cauchy-Green tensors, by imposing that they must stay on a submanifold of P sym, which we call reduced constraint manifold. We determine: all the constraint manifolds that are independent of the local reference configuration, a new formula for the reaction space, all the constraint manifolds whose reaction spaces are independent of the deformation gradient.