. "RIV/68378297:_____/07:00087614" . . "Praha" . "finite deformations; logarithmic strain; Riemannian geometry"@en . . "1"^^ . . . "1"^^ . "432385" . . "Na prostoru symetrick\u00FDch, pozitivn\u011B definintn\u00EDch matic (prostor deforma\u010Dn\u00EDch tenzor\u00F9) lze zav\u00E9st Riemannovu metriku tak, \u017Ee exponenci\u00E1la matice reprezentuje geodetiku, tj. zobecn\u011Bnou p\u0159\u00EDmku (nebo-li nejkrat\u0161\u00ED spojnici dvou bod\u00F9), vych\u00E1zej\u00EDc\u00ED z po\u00E8\u00E1te\u010Dn\u00EDho bodu - jednotkov\u00E9 matice, sm\u011Brem ur\u010Den\u00FDm vektorem - zadanou matic\u00ED. Uk\u00E1\u017Eeme, \u017Ee logaritmick\u00FD tenzor p\u0159etvo\u0159en\u00ED lze tak interpretovat jako vektor ur\u010Den\u00FD geodetikou, kter\u00E1 spojuje nedeformovan\u00FD a deformovan\u00FD stav."@cs . "On the space of all symmetric positive definite matrices (the space of deformation tensor fields) one can introduce a Riemannian geometry, so that the matrix exponential represents ageodesic (i.e. a generalised straight line, the shortest connecting line of two points) emanating from an initial point - the identity matrix, in a direction given by a vector - the prescribed matrix. Based on this approach, we prove that the logarithmic strain can be interpreted as a vector, determined by a geodesic connecting an undeformed and a deformed states." . "Fiala, Zden\u011Bk" . "Engineering Mechanics 2007" . "RIV/68378297:_____/07:00087614!RIV08-AV0-68378297" . . . "Exponenci\u00E1la matice a geometrick\u00FD v\u00FDznam pole logaritmick\u00E9ho tenzoru p\u0159etvo\u0159en\u00ED"@cs . "Matrix exponential and geometrical meaning of logarithmic strain"@en . "\u00DAstav termomechaniky AV \u010CR" . . "Exponenci\u00E1la matice a geometrick\u00FD v\u00FDznam pole logaritmick\u00E9ho tenzoru p\u0159etvo\u0159en\u00ED"@cs . "Z(AV0Z20710524)" . "Matrix exponential and geometrical meaning of logarithmic strain" . "10"^^ . . "2007-05-14+02:00"^^ . "Svratka" . "55;64" . . "[C9E29D15314B]" . . "978-80-87012-06-2" . "Matrix exponential and geometrical meaning of logarithmic strain"@en . . . "On the space of all symmetric positive definite matrices (the space of deformation tensor fields) one can introduce a Riemannian geometry, so that the matrix exponential represents ageodesic (i.e. a generalised straight line, the shortest connecting line of two points) emanating from an initial point - the identity matrix, in a direction given by a vector - the prescribed matrix. Based on this approach, we prove that the logarithmic strain can be interpreted as a vector, determined by a geodesic connecting an undeformed and a deformed states."@en . . "Matrix exponential and geometrical meaning of logarithmic strain" . .