Analysis of the theory of micropolar elasticity (micropolar)

Ehsan Eshghi¹

1) PhD Student in Mechanical Engineering, Applied Design, Islamic Azad University, Marvdasht Branch, Fars, Iran,

IOI Code : XEDC-GHKKA
Publication : 7th.International Conference on Researches in Science & Engineering & 4th.International Congress on Civil, Architecture and Urbanism in Asia(7icrsie.com)
Abstract :
    In this paper, a fast method for solving elasticity problems using the boundary component method is presented. The theory of classical linear elasticity has a long history of formation and validation and gives acceptable results in many engineering problems with various structural materials. However, for cases where the stress gradient is high (such as near cavities or cracks) or where the material has a significant contribution to the infrastructure (such as composites, polymers, soil and bone), the classical theory can not provide acceptable results. To improve the results of the classical theory, Voight considered the effects of coupling stresses and generalized the symmetric classical theory to the asymmetric coupling stress theory. Then, Eugene Casrat and François Casrat, who considered the microwave field of an object to be separate from the field of displacement of the object, generalized this theory. Eringen redeveloped the Cassratt model with the retrieval of a body object and named it the Theory of Polar (Asymmetric) Elasticity. Novaki provides a comprehensive explanation of the theory of linear micropolar elasticity. The theory of micropolar elasticity (micropolar) provides a practical model of materials for dealing with fibrous, coarse, and coarse-grained materials. Although the theory of linear micropolar elasticity is a well-known and well-codified model of elasticity, it is still a controversial topic. In particular, the discussion of the simplification of this theory to the theories of coupling and classical stress elasticity and the necessary conditions for the elastic constants of matter for this simplification has not been inconsistent. In this article, we will first review the theory of linear micropolar elasticity. Then, the correct method for step-by-step simplification of the micropolar elasticity model with 6 elastic constants is introduced to the coupling stress elasticity model with 4 elastic constants and the classical model with 2 elastic constants. It is proved that classical elasticity is a special case of coupling stress theory that the coupling stress theory itself is a special case of micropolar elasticity theory.

Keywords : application nonlinear theory of elasticity vibrations nanotubes