Variational formulations of non-linear and non-smooth structural problems (Q1261593)

The authors develop a variational formulation for non-smooth and nonlinear mechanical problems. This encompasses unilateral displacement constraints as well as multi-valued stress-strain constitutive laws, which are subdifferentials of convex stored energy functions of the strain. This is the main defect of an otherwise elegant theory: Convex stored energy functions are physically not possible, they violate the principle of material frame-indifference. This does not mean that a variational theory is not possible (polyconvexity would be a good starting point), but it will be more difficult than the present naive approach.