On the branching of solutions and Signorini's perturbation procedure in elasticity

Abstract

Signorini's perturbation method is a special case of a general technique, particularly adapted to a study of stability and branching phenomena in hyperelasticity. The interpretation already advanced[2] of the phenomena of incompatibility discovered by Signorini can be extended to apply to more general cases where the ground state is stressed and follower loads are present. In particular the well-known arbitrariness in the choice of amplitude of the buckled shapes within the first approximation can be interpreted either as a temporary freedom soon to be mitigated by conditions of compatibility of higher order systems or as a real scope in the choice of initial placements within the class of placements whence a motion begins where the acceleration is of higher order.