Počet záznamů: 1  

Evolution equation of Lie-type for finite deformations, time-discrete integration, and incremental methods

  1. 1. 0428756 - UTAM-F 2018 RIV AT eng J - Článek v odborném periodiku
    Fiala, Zdeněk
    Evolution equation of Lie-type for finite deformations, time-discrete integration, and incremental methods.
    Acta mechanica. Roč. 226, č. 1 (2015), s. 17-35. ISSN 0001-5970
    Grant CEP: GA ČR(CZ) GA103/09/2101
    Institucionální podpora: RVO:68378297
    Klíčová slova: solid mechanics * finite deformations * evolution equation of Lie-type * time-discrete integration
    Kód oboru RIV: BA - Obecná matematika
    Obor OECD: Statistics and probability
    Impakt faktor: 1.694, rok: 2015
    http://link.springer.com/article/10.1007%2Fs00707-014-1162-9#page-1

    While the position and shape of a deformed body take place in the usual three-dimensional Euclidean space, a corresponding progress of the deformation tensor makes up a trajectory in the space of all symmetric positive-definite matrices - a negatively curved Riemannian symmetric manifold. In this context, we prove that a well-known relation between deformation rate and symmetric velocity gradient, via deformation gradient, can be actually interpreted as an equation of Lie-type describing evolution of the right Cauchy-Green deformation tensor on the configuration space .As a consequence, this interpretation leads to geometrically consistent time-discrete integration schemes for finite deformation processes, such as the Runge-Kutta-Munthe-Kaas method. The need to solve such equation arises from an incremental numerical modelling of deformations of nonlinear materials.
    Trvalý link: http://hdl.handle.net/11104/0235626