Geometrical setting of solid mechanics |
| |
Authors: | Zdeněk Fiala |
| |
Affiliation: | The Institute of Theoretical and Applied Mechanics, ASCR, v. v. i., Prosecká 809/76, 190 00 Praha 9, Czech Republic |
| |
Abstract: | The starting point in the geometrical setting of solid mechanics is to represent deformation process of a solid body as a trajectory in a convenient space with Riemannian geometry, and then to use the corresponding tools for its analysis. Based on virtual power of internal stresses, we show that such a configuration space is the (globally) symmetric space of symmetric positive-definite real matrices. From this unifying point of view, we shall analyse the logarithmic strain, the stress rate, as well as linearization and intrinsic integration of corresponding evolution equation. |
| |
Keywords: | Solid mechanics Lagrangian system Riemannian symmetric space Logarithmic strain Linearization Time-discrete approximation |
本文献已被 ScienceDirect 等数据库收录! |
|