ABSTRACT
It was noted in Chapter 3 that lattices of beams should be modeled by micropolar, rather than classical, elastic continua. This chapter outlines the basic theory of such continuum models-both unrestricted and restricted (couple-stress) ones. In particular, we first provide a formulation of basic equations in 3D, and then, in analogy to Chapter 3, we focus on planar micropolar elasticity. Special attention is given to a generalization of the CLM result, and its consequences. Furthermore, we discuss the problem of homogenization of a heterogeneous Cauchy-type composite by a homogeneous micropolar-type material. If conducted properly, one may then reduce the number of degrees of freedom involved in, say, a finite element method, although the method would have to account for a micropolar nature of the approximating body. This also provides more physical insight into the so-called characteristic length, usually an enigmatic concept appearing (and vanishing) in papers on micropolar theories. Although several monographs have been written on the subject of micropolar media, most of the topics discussed in this chapter have never been collected in a book form.
