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.
机构:Univ of Illinois at Chicago, Dep of, Civil Engineering, Mechanics, &, Metallurgy, Chicago, IL, USA, Univ of Illinois at Chicago, Dep of Civil Engineering, Mechanics, & Metallurgy, Chicago, IL, US
机构:Univ of Illinois at Chicago, Dep of, Civil Engineering, Mechanics, &, Metallurgy, Chicago, IL, USA, Univ of Illinois at Chicago, Dep of Civil Engineering, Mechanics, & Metallurgy, Chicago, IL, US