We report on several numerical experiments where the rank-one convexification of an energy density is computed. The explicit examples cover a whole spectrum of typical situations one may encounter. One of those is especially relevant for the computation of microstructures in crystalline solids.

This paper deals with the problem of sensitivity analysis in calculus of variations. A perturbation technique is applied to derive the boundary value problem and the system of equations that allow us to obtain the partial derivatives (sensitivities) of the objective function value and the primal and dual optimal solutions with respect to all parameters. Two examples of applications, a simple mathematical problem and a slope stability analysis problem, are used to illustrate the proposed method.

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In this paper we study a numerical scheme for non-convex vector variational problems allowing for microstructure, based on the approximation of gradient Young measures. We present a convergence result and some numerical experiments.

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