Symmetric Cauchy stresses do not imply symmetric Biot strains in weak formulations of isotropic hyperelasticity with rotational degrees of freedom

From MaRDI portal
Publication:932012

DOI10.1007/s00707-007-0509-xzbMath1139.74007OpenAlexW2010806886MaRDI QIDQ932012

Patrizio Neff, Ingo Muench, Andreas Fischle

Publication date: 8 July 2008

Published in: Acta Mechanica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00707-007-0509-x




Related Items

On Grioli's minimum property and its relation to Cauchy's polar decompositionNumerical treatment of a geometrically nonlinear planar Cosserat shell modelWave propagation in relaxed micromorphic continua: modeling metamaterials with frequency band-gapsSimple shear in nonlinear Cosserat elasticity: bifurcation and induced microstructureGeometry of logarithmic strain measures in solid mechanicsBiot Stress and Strain in Thin-Plate Theory for Large DeformationsTransversely isotropic material: nonlinear Cosserat versus classical approachThe relaxed-polar mechanism of locally optimal Cosserat rotations for an idealized nanoindentation and comparison with 3D-EBSD experimentsGeometrically nonlinear FEM analysis of 6‐parameter resultant shell theory based on 2‐D Cosserat constitutive modelThe geometrically nonlinear Cosserat micropolar shear–stretch energy. Part I: A general parameter reduction formula and energy‐minimizing microrotations in 2DThe geometrically nonlinear Cosserat micropolar shear–stretch energy. Part II: Non‐classical energy‐minimizing microrotations in 3D and their computational validation***Optimality of the relaxed polar factors by a characterization of the set of real square roots of real symmetric matricesNew Thoughts in Nonlinear Elasticity Theory via Hencky’s Logarithmic Strain TensorThe minimization of matrix logarithms: on a fundamental property of the unitary polar factorExplicit Global Minimization of the Symmetrized Euclidean Distance by a Characterization of Real Matrices with Symmetric SquareExistence theorem for geometrically nonlinear Cosserat micropolar model under uniform convexity requirementsTheory and FE analysis for structures with large deformation under magnetic loadingCharacterization of the critical points for the shear-stretch strain energy of a Cosserat problemCounterexamples to Korn’s inequality with non-constant rotation coefficientsDerivation of a model of nonlinear micropolar plateQuadratic-stretch elasticityExistence of minimizers in the geometrically non-linear 6-parameter resultant shell theory with drilling rotations



Cites Work