A note on plane strain and plane stress problems for a new class of elastic bodies

Abstract: In this paper we explore the consequences of prescribing constitutive relations for elastic bodies wherein “deformations ” are given as functions of “stresses”. For this class of constitutive relations in, the particular case of small deformations, we study boundary value problems for plane strain and plane stresses, and we develop a weak formulation that can be considered as the starting point for numerical computations