Many-field theory for crystals containing particles with rotational degrees of freedom

TL;DR

This paper reviews generalized continuum theories for crystals with complex microstructures, focusing on high-gradient, micropolar, and many-field theories, and discusses their applications through 1D and 2D examples.

Contribution

It introduces the many-field theory for crystals with particles possessing rotational degrees of freedom, highlighting its potential development and application.

Findings

High-gradient and micropolar theories are well-established.

Many-field theory is still under development.

Examples illustrate where each theory is applicable.

Abstract

We give a brief review of some generalized continuum theories applied to the crystals with complicated microscopic structure. Three different ways of generalization of the classical elasticity theory are discussed. One is the high-gradient theory, another is the micropolar type theory and the third one is the many-field theory. The importance of the first two types of theories has already been established, while the theory of the third type still has to be developed. With the use of 1D and 2D examples we show for each of these theories where they can be and should be applied, separately or in a combination.