Geometrically nonlinear Cosserat micropolar elasticity
Lead Research Organisation:
University College London
Department Name: Mathematics
Abstract
Research Area: Continuum mechanics
Continuum mechanics is a branch of mechanics that studies the mechanical behaviour of materials. These materials are modelled as a continuum rather than as a collection of discrete particles. This project studies the geometrical and physical properties of geometrically nonlinear Cosserat continua, there are often referred to as continuua with microstructue. The basic idea of this approach is to replace the idealised material point with an object with an additional structure. In ordinary solid mechanics or continuum mechanics, the material points are assumed to be structureless. These ideas go back to the Cosserat (1909) brothers who proposed a mathematical formulation to study such materials.
The project will study various aspects of Cosserat elasticity, starting with its formulation and alternative mathematical descriptions which can be applied to this model. Based on previous work, wave-like solutions will be studied exploiting the underlying geometrical structure of the equations. In particular it should be possible to find an explicit soliton-like solution of the fully nonlinear problem.
Cosserat elasticity also shows similarities with models previously studied in theoretical physical physics, part of this project aims at studying these models from a continuum mechanics point of of view. It is hoped to this new perspective will allow a new interpretation of these models. In particular, some results indicate that it should be possible to make connections between objects commonly used in elasticity and topological quantities.
Continuum mechanics is a branch of mechanics that studies the mechanical behaviour of materials. These materials are modelled as a continuum rather than as a collection of discrete particles. This project studies the geometrical and physical properties of geometrically nonlinear Cosserat continua, there are often referred to as continuua with microstructue. The basic idea of this approach is to replace the idealised material point with an object with an additional structure. In ordinary solid mechanics or continuum mechanics, the material points are assumed to be structureless. These ideas go back to the Cosserat (1909) brothers who proposed a mathematical formulation to study such materials.
The project will study various aspects of Cosserat elasticity, starting with its formulation and alternative mathematical descriptions which can be applied to this model. Based on previous work, wave-like solutions will be studied exploiting the underlying geometrical structure of the equations. In particular it should be possible to find an explicit soliton-like solution of the fully nonlinear problem.
Cosserat elasticity also shows similarities with models previously studied in theoretical physical physics, part of this project aims at studying these models from a continuum mechanics point of of view. It is hoped to this new perspective will allow a new interpretation of these models. In particular, some results indicate that it should be possible to make connections between objects commonly used in elasticity and topological quantities.
Organisations
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| EP/N509577/1 | 01/10/2016 | 24/03/2022 | |||
| 1916529 | Studentship | EP/N509577/1 | 01/10/2017 | 30/09/2021 | Yongjo Lee |
| Description | The deformation in a body can be described by both in macroscopic observation and microscopic observation. Macroscopic deformational descriptions are often said to be classical theory of deformation and it is well-studied subject. While, the microscopic deformation theory of the body is thought to be independent to the macroscopic deformation and it plays an important role in many fields in both of physics and engineering studies. We found that the microscopic deformation is governed by a soliton wave motion. A soliton wave is a solitary wave which propagate through the medium without changing its shape, hence the energy value, as time goes by. Once this deformational wave as a form of soliton wave pass through the body will return to its original configuration. This particular description is said to be elastic deformation. Chirality is an asymmetric property (e.g. left hand and right hand are asymmetric as a mirror image to each other) appears in many physical subfields. It was belied that the chiral property in three dimensions will be lost when the body is projected into the plane. But we found that this soliton wave pertain the specific property that preserve the chirality in the plane if we construct the energy function in a particular way to achieve this conservation. |
| Exploitation Route | The above mentioned studies of microscopic deformational theory is strongly related to other subfields such as condensed matter physics or low energy condensations in describing the defects in the medium. Most notably this study can be a good candidate in studying the microscopic deformational description of vacuum spacetime itself in connection with the general relativity. This can be done if one sees the spacetime as a deformable body which is affected by the presence of matter distribution but with the microscopic deformation which can be viewed as a higher order than the conventional macroscopic defects. |
| Sectors | Other |
| URL | https://www.sciencedirect.com/science/article/pii/S0165212518302208 |