Quasiconvexity in a model of fiber-reinforced solids based on Cosserat elasticity theory

The quasiconvexity inequality associated with energy minimizers is derived in the context of a nonlinear Cosserat elasticity theory for fiber-reinforced elastic solids in which the intrinsic flexural and torsional elasticities of the fibers are taken into account explicitly. The derivation accounts for non-standard kinematic constraints, associated with the materiality of the embedded fibers, connecting the deformation gradient and the Cosserat rotation field.