A plane nonlinear shear for elastic layer with a nonconvex stored energy function
In the present work we consider a specific and elementary minimization problem in which the nonconvexity of the stored energy function manifests itself as a novel phenomenon. In particular, in this problem an elastic layer is bonded between two infinite parallel rigid plates and the plates are rotated in the same sense through the same angle about distinct axes normal to the plates. In general the shear that is thereby induced in the layer is expected to correspond to the relative rotation of planes of material throughout the thickness of the layer and about centers which are dependent upon the position of these planes of two distinct slopes. In this latter case there is considerable nonuniqueness with respect to how the combination of straight line segments may be arranged without affecting the energy of the system. The general structure of all minimizers in this problem is completely determined.
nonconvexity of the stored energy function
scientific article; zbMATH DE number 3970242