Computation of the lower semicontinuous envelope of integral functionals and non-homogeneous microstructures

A numerical method is established for computing the weakly lower semicontinuous envelope of integral functionals with non-quasiconvex integrands. The convergence of the method is proved and it is shown that the method is capable of capturing curved and non-homogeneous microstructures. Numerical examples are given to show the effectiveness of the method for capturing curved and non-homogeneous laminated microstructures.