Discrete and Multifield Models of a Cosserat Chain: One-Period and Two-Period Solutions

Abstract

A multifield theory of bodies with microstructure is developed. As the basic model we take the structural model of a Cosserat chain consisting of particles of rectangular shape. A linear complete discrete model, a linear reduced discrete model, and a nonlinear discrete model are derived and discussed. One-period and two-period solutions are obtained, describing small oscillations of particles in one direction and in different directions. Single-field and two-field, complete and reduced Cosserat models are constructed. It is shown that the singlefield model describes one-period solutions in the chain while the two-field model describes both long-wave one-period and short-wave two-period solutions.