The geometrically nonlinear Cosserat micropolar shear–stretch energy. Part I: A general parameter reduction formula and energy‐minimizing microrotations in 2D

DOI10.1002/zamm.201500194arXiv1507.05480OpenAlexW2964202678MaRDI QIDQ6066709

Andreas Fischle, Patrizio Neff

Publication date: 13 December 2023

Published in: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.05480

zbMATH Keywords

polar decompositionmicropolarCosseratGrioli's theoremnon-symmetric stretchpolar mediazero Cosserat couple modulusEuclidean distance to \(\mathrm{SO}(n)\)

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Energy minimization in equilibrium problems in solid mechanics (74G65) Matrix equations and identities (15A24) Polar materials (74A35) Nonsimple materials (74A30) Explicit solutions of equilibrium problems in solid mechanics (74G05) Analysis of microstructure in solids (74N15)

Related Items (3)

The relaxed-polar mechanism of locally optimal Cosserat rotations for an idealized nanoindentation and comparison with 3D-EBSD experiments ⋮ Optimality of the relaxed polar factors by a characterization of the set of real square roots of real symmetric matrices ⋮ Characterization of the critical points for the shear-stretch strain energy of a Cosserat problem

Cites Work

• Unnamed Item
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• Geometry of logarithmic strain measures in solid mechanics
• A finite-strain elastic-plastic Cosserat theory for polycrystals with grain rotations
• On vectorially parameterized natural strain measures of the nonlinear Cosserat continuum
• Existence theorem for geometrically nonlinear Cosserat micropolar model under uniform convexity requirements
• Simple shear in nonlinear Cosserat elasticity: bifurcation and induced microstructure
• Symmetric Cauchy stresses do not imply symmetric Biot strains in weak formulations of isotropic hyperelasticity with rotational degrees of freedom
• A shell theory with independent rotations for relaxed Biot stress and right stretch strain
• Finite multiplicative plasticity for small elastic strains with linear balance equations and grain boundary relaxation
• Second-order shell kinematics implied by rotation constraint-equation
• Kinematics of finite rotation shells with in-plane twist parameter
• On Grioli's minimum property and its relation to Cauchy's polar decomposition
• Stable identification of linear isotropic Cosserat parameters: bounded stiffness in bending and torsion implies conformal invariance of curvature
• Soliton-like solutions based on geometrically nonlinear Cosserat micropolar elasticity
• The minimization of matrix logarithms: on a fundamental property of the unitary polar factor
• Existence of minimizers in the geometrically non-linear 6-parameter resultant shell theory with drilling rotations
• A Logarithmic Minimization Property of the Unitary Polar Factor in the Spectral and Frobenius Norms
• The Cosserat couple modulus for continuous solids is zero viz the linearized Cauchy-stress tensor is symmetric
• A new paradigm: the linear isotropic Cosserat model with conformally invariant curvature energy
• An Elementary Proof of the Polar Decomposition Theorem
• Direct determination of the rotation in the polar decomposition of the deformation gradient by maximizing a Rayleigh quotient
• Curl bounds Grad on SO(3)

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