Direct determination of the rotation in the polar decomposition of the deformation gradient by maximizing a Rayleigh quotient

DOI10.1002/zamm.200310167zbMath1155.74306OpenAlexW2067977633MaRDI QIDQ4667683

Danielle Fortuné, Céline Bouby, Wojciech Pietraszkiewicz, Claude Vallee

Publication date: 21 April 2005

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://doi.org/10.1002/zamm.200310167

zbMATH Keywords

rotation Rayleigh quotient conjugate gradient algorithm continuum mechanics polar decomposition quaternion

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Generalities, axiomatics, foundations of continuum mechanics of solids (74A99)

Related Items (12)

A new deformation measure for the nonlinear micropolar continuum ⋮ On Grioli's minimum property and its relation to Cauchy's polar decomposition ⋮ An algorithm to compute the polar decomposition of a \(3 \times 3\) matrix ⋮ Geometry of logarithmic strain measures in solid mechanics ⋮ The geometrically nonlinear Cosserat micropolar shear–stretch energy. Part I: A general parameter reduction formula and energy‐minimizing microrotations in 2D ⋮ \(\mathbf{U} = \mathbf{C}^{1/2}\) and its invariants in terms of \(\mathbf{C}\) and its invariants ⋮ New Thoughts in Nonlinear Elasticity Theory via Hencky’s Logarithmic Strain Tensor ⋮ On the global interpolation of motion ⋮ Explicit representation for the \(\mathrm{SO}(3)\) rotation tensor of deformable bodies ⋮ Spectral collocation methods for the periodic solution of flexible multibody dynamics ⋮ Quadratic-stretch elasticity ⋮ Polar rotation angle identifies elliptic islands in unsteady dynamical systems

Cites Work

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