Invariants of C1∕2 in terms of the invariants of C

Norris, Andrew

doi:10.2140/jomms.2007.2.1805

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Invariants of ${C}^{1/2}$ in terms of the invariants of $C$

Andrew N. Norris

Vol. 2 (2007), No. 9, 1805–1812

DOI: 10.2140/jomms.2007.2.1805

Abstract

The three invariants of $C^{1 ∕ 2}$ are key to expressing this tensor and its inverse as a polynomial in $C$ . Simple and symmetric expressions are presented connecting the two sets of invariants ${I_{1}, I_{2}, I_{3}}$ and ${i_{1}, i_{2}, i_{3}}$ of $C$ and $C^{1 ∕ 2}$ , respectively. The first result is a bivariate function relating $I_{1}, I_{2}$ to $i_{1}, i_{2}$ . The functional form of $i_{1}$ is the same as that of $i_{2}$ when the roles of the $C$ -invariants are reversed. The second result expresses the invariants using a single function call. The two sets of expressions emphasize symmetries in the relations among these four invariants.

Keywords

invariants, finite elasticity, stretch tensors, polar decomposition

Milestones

Received: 11 January 2007

Revised: 4 March 2007

Accepted: 4 June 2007

Published: 1 November 2007

Authors

Andrew N. Norris
Rutgers University Mechanical and Aerospace Engineering 98 Brett Road Piscataway, NJ 08854-8058 United States
http://mechanical.rutgers.edu/norris

Vol. 2, No. 9, 2007

Andrew N. Norris

Abstract

Keywords

Milestones

Authors