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Evolution equation of Lie-type for finite deformations, time-discrete integration, and incremental methods
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SYSNO ASEP 0428756 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Evolution equation of Lie-type for finite deformations, time-discrete integration, and incremental methods Author(s) Fiala, Zdeněk (UTAM-F) RID, ORCID, SAI Number of authors 1 Source Title Acta Mechanica. - : Springer - ISSN 0001-5970
Roč. 226, č. 1 (2015), s. 17-35Number of pages 19 s. Publication form Print - P Language eng - English Country AT - Austria Keywords solid mechanics ; finite deformations ; evolution equation of Lie-type ; time-discrete integration Subject RIV BA - General Mathematics OECD category Statistics and probability R&D Projects GA103/09/2101 GA ČR - Czech Science Foundation (CSF) Institutional support UTAM-F - RVO:68378297 UT WOS 000347282300002 EID SCOPUS 84958038901 DOI 10.1007/s00707-014-1162-9 Annotation 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. Workplace Institute of Theoretical and Applied Mechanics Contact Kulawiecová Kateřina, kulawiecova@itam.cas.cz, Tel.: 225 443 285 Year of Publishing 2018 Electronic address http://link.springer.com/article/10.1007%2Fs00707-014-1162-9#page-1
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