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 {I₁,I₂,I₃} and {i₁,i₂,i₃} of C and C^{1 ∕ 2}, 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.

Keywords

invariants, finite elasticity, stretch tensors, polar decomposition

Authors