Equilibrium configurations of mixture thin films undergoing large strains

摘要: We describe a mixture thin film as membrane endowed with multiple out-of-tangent-plane vectors at each point, vector sequence defined to within permutation account for the mixing of components. Such description is motivated by proposal an atomistic-to-continuum derivation representation multiatomic layer films, view not requiring introduction phenomenological parameters. Differences between that and model discussed here are definition values layer-descriptor map permutations explicit bending-like term in energy. The satisfy condition forbidding them fall tangent plane after deformation. consider generic weakly surface-polyconvex energy quadratic bending involving vectors, which also quasiconvex. Under appropriate growth assumptions Dirichlet-type boundary conditions, we prove existence ground states, i.e., equilibrium configurations described solutions balance equations. An obvious corollary single Cosserat surfaces, natural scheme plates simple materials.