000009216 001__ 9216 000009216 005__ 20141204092419.0 000009216 04107 $$aeng 000009216 046__ $$k12/05/2014 000009216 100__ $$aFiala, Z. 000009216 24500 $$aTime-discrete integration of finite deformation 000009216 24630 $$n18.$$pEngineering Mechanics 2012 000009216 260__ $$bInstitute of Theoretical and Applied Mechanics, AS CR, Prague 000009216 506__ $$arestricted 000009216 520__ $$2eng$$aSome necessary implications for the time-discrete integration of finite deformations will be discussed together with particular schemes, when the geometrical structure of the space of Cauchy-Green deformation tensors, implicitly contained in the principle of virtual power, is taken into account. All these time-discrete schemes reflect this geometrical structure in that the actual integration of corresponding evolution equation of deformation process takes place in the subset of positive-definite symmetric matrices (with non-euclidean geometry) by definition, instead of in the linear space of symmetric matrices (with euclidean geometry) as usual. 000009216 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb. 000009216 653__ $$afinite deformation, time-discrete integration, Runge –Kutta – Munthe-Kaas method 000009216 7112_ $$aEngineering Mechanics 2012$$cSvratka (CZ)$$d12/05/2014 - 15/05/2014$$gEM2012 000009216 720__ $$aFiala, Z. 000009216 8560_ $$ffischerc@itam.cas.cz 000009216 8564_ $$s309366$$uhttps://invenio.itam.cas.cz/record/9216/files/164_Fiala_Z-FT.pdf$$yOriginal version of the author's contribution as presented on CD, paper (No. 164). 000009216 962__ $$r8924 000009216 980__ $$aPAPER