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.


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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