Symmetric Cauchy stresses do not imply symmetric Biot strains in weak formulations of isotropic hyperelasticity with rotational degrees of freedom
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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
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Cites Work
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- A finite-strain elastic-plastic Cosserat theory for polycrystals with grain rotations
- On drilling degrees of freedom
- On the rank 1 convexity of stored energy functions of physically linear stress-strain relations
- A shell theory with independent rotations for relaxed Biot stress and right stretch strain
- Formulations of finite elasticity with independent rotations
- A unifying treatise of variational principles for two types of micropolar continua
- A variational formulation for finite elasticity with independent rotation and Biot-axial fields
- On drilling degrees of freedom in nonlinear elasticity and a hyperelastic material description in terms of the stretch tensor. I: Theory
- On isotropic functions of symmetric tensors, skew-symmetric tensors and vectors
- A geometrically exact micromorphic model for elastic metallic foams accounting for affine microstructure. Modelling, existence of minimizers, identification of moduli and computational results
- Existence of minimizers for a geometrically exact Cosserat solid
- A robust quadrilateral membrane finite element with drilling degrees of freedom
- The Cosserat couple modulus for continuous solids is zero viz the linearized Cauchy-stress tensor is symmetric
- Existence of minimizers for a finite-strain micromorphic elastic solid
- The Biot stresses in nonlinear elasticity and the associated generalized variational principles