Vol. 2, No. 9, 2007

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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

The three invariants of C12 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 {I1,I2,I3} and {i1,i2,i3} of C and C12, respectively. The first result is a bivariate function relating I1,I2 to i1,i2. The functional form of i1 is the same as that of i2 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.

invariants, finite elasticity, stretch tensors, polar decomposition
Received: 11 January 2007
Revised: 4 March 2007
Accepted: 4 June 2007
Published: 1 November 2007
Andrew N. Norris
Rutgers University
Mechanical and Aerospace Engineering
98 Brett Road
Piscataway, NJ 08854-8058
United States