Search
Abstract
As part of his groundbreaking work on generalized continuum mechanics, Eringen proposed what he called 3M theories, namely the concept of micromorphic, microstretch, and micropolar materials modeling. The micromorphic approach provides the most general framework for a continuum with translational and (internal) rotational degrees of freedom (DOF), whilst the rotational DOFs of micromorphic and micropolar continua are subjected to more and more constraints. More recently, an “extended” micropolar theory has been presented by one of the authors: Eringen’s 3M theories were children of solid mechanics based on the concept of the indestructible material particle. Extended micropolar theory was formulated both ways for material systems as well as in spatial description, which is useful when describing fluid matter. The latter opens the possibility to model situations and materials with a continuum point that on the microscale consists no longer of the same elementary units during a physical process. The difference culminates in an equation for the microinertia tensor, which is no longer a kinematic identity. Rather it contains a new continuum field, namely an independent production term and, consequently, establishes a new constitutive quantity. This makes it possible to describe processes of structural change, which are difficult if not impossible to be captured within the material particle model. This paper compares the various theories and points out their communalities as well as their differences.
Citations
-
1 0
CrossRef
-
0
Web of Science
-
9
Scopus
Authors (3)
-
Elena Vilchevskaya Dr hab
-
Wolfgang Müller Dr hab rer nat
Cite as
Full text
- Publication version
- Accepted or Published Version
- DOI:
- Digital Object Identifier (open in new tab) 10.1007/s00161-021-01072-6
- License
-
open in new tab
Keywords
Details
- Category:
- Articles
- Type:
- artykuły w czasopismach
- Published in:
-
CONTINUUM MECHANICS AND THERMODYNAMICS
no. 34,
pages 533 - 554,
ISSN: 0935-1175 - Language:
- English
- Publication year:
- 2022
- Bibliographic description:
- Vilchevskaya E., Müller W., Eremeev V.: Extended micropolar approach within the framework of 3M theories and variations thereof// CONTINUUM MECHANICS AND THERMODYNAMICS -Vol. 34,iss. 5 (2022), s.533-554
- DOI:
- Digital Object Identifier (open in new tab) 10.1007/s00161-021-01072-6
- Sources of funding:
-
- Free publication
- Verified by:
- Gdańsk University of Technology
seen 111 times
Recommended for you
On rotational instability within the nonlinear six-parameter shell theory
- J. Chróścielewski,
- F. Dell’isola,
- V. Eremeyev
- + 1 authors