Nonlinear Cauchy Elasticity
Most theories and applications of elasticity rely on an energy function that depends on the strains from which the stresses can be derived. This is the traditional setting of Green elasticity, also known as hyper-elasticity. However, in its original form the theory of elasticity does not assume the existence of a strain energy function. In this case, called Cauchy elasticity, stresses are directly related to the strains. Since the emergence of modern elasticity in the 1940s, research on Cauchy elasticity has been relatively limited.
