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Non-convex variational/boundary-value problems are studied using a modified version of the Ericksen bar model in nonlinear elasticity. The strain-energy function is a general fourth-order polynomial in a suitable measure of strain that provides a convenient model for the study of, for example, phase transitions. On the basis of a canonical duality theory, the nonlinear differential equation for th...

Multiple solutions to non-convex variational problems with implications for phase transitions and numerical computation