000001761 001__ 1761
000001761 005__ 20141118153455.0
000001761 04107 $$acze
000001761 046__ $$k2010-05-10
000001761 100__ $$aFiala, Z.
000001761 24500 $$aLogarithmic strain in 1 versus 3(2) dimensions

000001761 24630 $$n16$$pEngineering Mechanics 2010
000001761 260__ $$bInstitute of Thermomechanics AS CR, v.v.i., Prague
000001761 506__ $$arestricted
000001761 520__ $$2eng$$aThe paper discusses the logarithmic strain in one dimension (1D) from the geometrical point of view to highlight the nature of problems when generalizing it to more dimensions (3D or 2D). Starting from geometry of positive real numbers R+, author advocates the geometrical approach via the Riemannian geometry of the space of symmetric positive-definite n×n matrices (n stands for dimension) of real numbers Sym+ (n, R) ∼ GL+ (n, R)/SO(n, R), which reduces to R+ in the case = of 1D. Based on previous papers, he demonstrates that only such an approach can guarantee consistent and well-defined manipulation with the logarithmic strain in more dimensions. Even though the geometry itself is rather unusual and nonintuitive due to its non-euclidean nature, its profit for the theory of finite deformations is noticeable and has already been demonstrated formerly – the natural and unambiguous linearization for an incremental approach within finite deformations, based on covariant derivative instead of on one of many objective time derivatives.

000001761 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000001761 653__ $$a

000001761 7112_ $$aEngineering Mechanics 2010$$cSvratka (CZ)$$d2010-05-10 / 2010-05-13$$gEM2010
000001761 720__ $$aFiala, Z.
000001761 8560_ $$ffischerc@itam.cas.cz
000001761 8564_ $$s307079$$uhttps://invenio.itam.cas.cz/record/1761/files/Fiala-083-PT.pdf$$y
             Original version of the author's contribution as presented on CD, SOL.
            
000001761 962__ $$r1750
000001761 980__ $$aPAPER