Multi-field approach in mechanics of structural solids

TL;DR

This paper reviews the multi-field continuum theory for complex structural solids, introducing macrocell-based models that extend classical theories to short-wavelength deformations, with applications and future directions discussed.

Contribution

It develops a multi-field continuum framework for structural solids, generalizing classical models to account for complex structures and short-wavelength phenomena.

Findings

Multi-field models capture short-wavelength deformations.

Comparison shows models extend classical continuum theories.

Applications demonstrate the approach's versatility.

Abstract

We overview the basic concepts, models, and methods related to the multi-field continuum theory of solids with complex structures. The multi-field theory is formulated for structural solids by introducing a macrocell consisting of several primitive cells and, accordingly, by increasing the number of vector fields describing the response of the body to external factors. Using this approach, we obtain several continuum models and explore their essential properties by comparison with the original structural models. Static and dynamical problems as well as the stability problems for structural solids are considered. We demonstrate that the multi-field approach gives a way to obtain families of models that generalize classical ones and are valid not only for long-, but also for short-wavelength deformations of the structural solid. Some examples of application of the multi-field theory and directions for its further development are also discussed.