Some relaxation results for functionals depending on constrained strain and chemical composition

We prove some relaxation results in the spirit of Anza Hafsa and Mandallena for integral functionals arising in the study of coherent thermochemical equilibria for multiphase solids. The energy density exhibits an explicit dependence on the deformation gradient and on a vector field representing the chemical composition. The deformation gradient satisfies a determinant type constraint and the chemical composition a constraint on the modulus. To cite this article: E. Zappale, H. Zorgati, C. R. Acad. Sci. Paris, Ser. I 347 (2009).