A mixed Cosserat and higher gradient formulation for fibrous tissues and biomaterials

Fibrous materials, including engineering composites and biological tissues, exhibit distinctive behaviors that can be characterized by melding concepts of Cosserat and higher gradient elasticities. In this work, we generalize higher gradient theories for fibrous materials by considering Cosserat effects. We use the principle of virtual power and the calculus of variations to obtain the balance laws and boundary conditions. For minimizing the total potential energy of the system, we find conditions for quasi-convexity, rank-one convexity, and Legendre-Hadamard inequalities that must be satisfied for solutions of the balance laws to be valid. Finally, we present a linearized formulation and show illustrative computational results. According to one example, Poynting effects arise from non-classical effects such as higher gradients and Cosserat effects.