A Generalized Continuum Theory and Its Relation to Micromorphic Theory

Abstract

Classic continuum mechanics views a crystal as a homogeneous and continuous medium, in which the basic structural unit of the crystal is taken without structure and is idealized as point mass. Micromorphic theory views a material as a continuous collection of deformable point particles; each particle has finite size and additional nine internal degrees of freedom describing the stretches and rotations of the particle. This paper presents a multiscale field theory that views a crystalline material as a continuous collection of lattice points, while embedded within each point is a group of discrete atoms. The atomistic formulation of the field theory is briefly introduced. Its relation with the well-known micromorphic theory is derived. The applicability of the classical continuum theory, micromorphic theory, and the generalized continuum field theory is discussed.