Evolution equation of Lie-type for finite deformations, time-discrete integration, and incremental methods
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68378297%3A_____%2F15%3A00428756" target="_blank" >RIV/68378297:_____/15:00428756 - isvavai.cz</a>
Result on the web
<a href="http://link.springer.com/article/10.1007%2Fs00707-014-1162-9#page-1" target="_blank" >http://link.springer.com/article/10.1007%2Fs00707-014-1162-9#page-1</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00707-014-1162-9" target="_blank" >10.1007/s00707-014-1162-9</a>
Alternative languages
Result language
angličtina
Original language name
Evolution equation of Lie-type for finite deformations, time-discrete integration, and incremental methods
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10103 - Statistics and probability
Result continuities
Project
<a href="/en/project/GA103%2F09%2F2101" target="_blank" >GA103/09/2101: Evaluation of the energy responsible for fracture advancing</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Acta mechanica
ISSN
0001-5970
e-ISSN
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Volume of the periodical
226
Issue of the periodical within the volume
1
Country of publishing house
AT - AUSTRIA
Number of pages
19
Pages from-to
17-35
UT code for WoS article
000347282300002
EID of the result in the Scopus database
2-s2.0-84958038901