On the Existence of Rotationally Symmetric Solution of a Constrained Minimization Problem of Elasticity

We consider the equilibrium problem, with no body force, of a cylindrically orthotropic disk subject to a prescribed displacement along its boundary. In classical linear elasticity, the solution of this problem predicts material overlapping, which is not physically realistic. One way to prevent this anomalous behavior is to consider the minimization of the total potential energy of classical linear elasticity subject to the local injectivity constraint. In the context of this constrained minimization theory, bifurcation occurs from a radially symmetric solution to a secondary solution. In this work we present analytical and computational results indicating that this secondary solution is rotationally symmetric.