On hyperelasticity for clays

Under purely elastic conditions a constitutive model for clays should be conservative. This can be achieved by using a hyperelastic stress–strain relation derived from an elastic potential. To circumvent problems connected with formulation of a suitable potential a simple concept of back-stress elasticity is proposed. Several elastic models are critically reviewed, two of which had been originally incorrectly classified as hyperelastic. A novel elastic potential which can be used to generate various hyperelastic models is proposed. Its salient feature is that the resulting stiffness is a homogeneous function of order 1 with respect to stress. An example of Mathematica calculation with tensorial differentiation is enclosed (Wolfram S. Mathematica. A system for doing mathematics by computer. Addison-Wesley Publishing, 1988). ©