Geometrical setting of solid mechanics

0360074 - ÚTAM 2012 RIV NL eng J - Článek v odborném periodiku
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
Grant CEP: GA ČR(CZ) GA103/09/2101
Výzkumný záměr: CEZ:AV0Z20710524
Klíčová slova: solid mechanics * Lagrangian system * time-discrete approximation
Kód oboru RIV: BE - Teoretická fyzika
Impakt faktor: 2.857, rok: 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.
Trvalý link: http://hdl.handle.net/11104/0197712