The significance of projection operators in the spectral representation of symmetric second order tensors

DOI10.1016/0045-7825(90)90078-ZzbMath0733.73002MaRDI QIDQ809649

M. B. Rubin, Charles P. Luehr

Publication date: 1990

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

zbMATH Keywords

repeated eigenvaluesN-dimensional Euclidean space

Mathematics Subject Classification ID

Crystalline structure (74E15) Applications of global differential geometry to the sciences (53C80)

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Cites Work

• Unnamed Item
• Determination of \(C^{1/2}\), \(C^{-1/2}\) and more general isotropic tensor functions of C
• Quasi-incompressible finite elasticity in principal stretches. Continuum basis and numerical algorithms
• Determination of the stretch and rotation in the polar decomposition of the deformation gradient