Geometrical setting of solid mechanics

0360074 - ÚTAM 2012 RIV NL eng J - Journal Article
Fiala, Zdeněk
Geometrical setting of solid mechanics.
Annals of Physics. Roč. 326, č. 8 (2011), s. 1983-1997. ISSN 0003-4916. E-ISSN 1096-035X
R&D Projects: GA ČR(CZ) GA103/09/2101
Institutional research plan: CEZ:AV0Z20710524
Keywords : solid mechanics * Lagrangian system * time-discrete approximation
Subject RIV: BE - Theoretical Physics
Impact factor: 2.857, year: 2011

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.
Permanent Link: http://hdl.handle.net/11104/0197712