Geometry of finite deformations and time-incremental analysis

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Geometry of finite deformations and time-incremental analysis

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Geometry of finite deformations and time-incremental analysis

Popis výsledku anglicky

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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BE - Teoretická fyzika

OECD FORD obor

—

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2016

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

International Journal of Non-Linear Mechanics

ISSN

0020-7462

e-ISSN

—

Svazek periodika

81

Číslo periodika v rámci svazku

May

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

15

Strana od-do

230-244

Kód UT WoS článku

000373538500023

EID výsledku v databázi Scopus

2-s2.0-84975110719