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Numerical approach to double well problems. (English) Zbl 0929.49016
The author considers stored energy densities \(W : \{F\in R^{2\times 2}\mid \text{det} F>0\}\rightarrow\) \(R\), when \(W\) satisfies the frame indifference principle, and has a double well structure. Different algorithms and numerical computations are presented for the approximation of the rank-one convex envelope of \(W\), and of the polyconvex envelope of \(W\), when the two wells are not necessarily rank-one connected. Problems are discretized by a finite element method, and sequential quadratic routines are used for the discrete minimization problems.

MSC:
49M99 Numerical methods in optimal control
65K10 Numerical optimization and variational techniques
49J35 Existence of solutions for minimax problems
74B20 Nonlinear elasticity
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