Mechanics of micromorphic materials

Abstract

In several previous papers [1, 2, 3], we presented some properly invariant nonlinear continuum theories of micro-elastic solids and micro-fluids in which the first stress moments, micro-stress averages and inertial spin play important roles. In the present paper we extend some of these ideas in the formulation of continuum mechanics of micromorphic materials in which the local micro-structure and intrinsic motions of the material are important. While it employs some simple statistical averages, the theory presented is not based on molecular theories and statistical mechanics but on a continuum theory. The foundation of the theory is consistent with the known principles of mechanics and a properly invariant theory of constitutive equations. It is believed that the theory has great promise in explaining many new phenomena hitherto unknown or treated partly through statistical mechanical approach in desperation. To name a few, the theory is capable of explaining the phenomenon of surface tension, couple stress, inertial spin, distributed vortices and micro-anisotropy in oriented materials, and it provides a firm foundation for the theory of polar materials. All of the classical theories of solids and fluids are included in the theory of micromorphic materials. Nevertheless, the ultimate success of the theory will have to be judged on the future outcome of rational experiments.