Geometry of finite deformations and time-incremental analysis
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68378297%3A_____%2F16%3A00456940" target="_blank" >RIV/68378297:_____/16:00456940 - isvavai.cz</a>
Result on the web
<a href="http://www.sciencedirect.com/science/article/pii/S0020746216000330" target="_blank" >http://www.sciencedirect.com/science/article/pii/S0020746216000330</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.ijnonlinmec.2016.01.019" target="_blank" >10.1016/j.ijnonlinmec.2016.01.019</a>
Alternative languages
Result language
angličtina
Original language name
Geometry of finite deformations and time-incremental analysis
Original language description
In connection with the origin of computational mechanics and consequent progress of incremental methods, a fundamental problem came up even in solid mechanics - namely how to correctly time-linearize and time-integrate deformation processes within finite deformations. Contrary to small deformations (actually infinitesimal), which represent a correction of an initial configuration in terms of tensor fields and so a description by means of a linear vector space of all symmetric matrices sym(3,R) is well-fitting, a situation with finite deformations is rather more complicated. In fact, while the position and shape of a deformed body take place in the usual three-dimensional Euclidean space R3, a corresponding progress of deformation tensor makes up a trajectory in Sym+(3,R) - a negatively curved Riemannian symmetric manifold. Since this space is not a linear vector space, we cannot simply employ tools from the theory of small deformations, but in order to analyze deformation processes correctly, we have to resort to the corresponding tools from the differential geometry and Lie group theory which are capable of handling the very geometric nature of this space. The paper first briefly recalls a common approach to solid mechanics and then its formulation as a simple Lagrangian system with configuration space Sym+(3,R). After a detailed exposition of the geometry of the configuration space, we finally sum up its consequences for the time-incremental analysis, resulting in clear and unambiguous conclusions.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BE - Theoretical physics
OECD FORD branch
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Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
International Journal of Non-Linear Mechanics
ISSN
0020-7462
e-ISSN
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Volume of the periodical
81
Issue of the periodical within the volume
May
Country of publishing house
GB - UNITED KINGDOM
Number of pages
15
Pages from-to
230-244
UT code for WoS article
000373538500023
EID of the result in the Scopus database
2-s2.0-84975110719