Abstract: We investigate objective corotational rates satisfying an additional, physically plausible assumption. More precisely, we require for D◦Dt[B] = A◦(B).D that the characteristic stiffness tensor A◦(B) is positive-definite. Here, B = F FT is the left Cauchy–Green tensor, D◦Dt is a specific objective corotational rate, D = sym Dξ v is the Eulerian stretching and A◦(B) is the corresponding induced characteristic fourth-order stiffness tensor. Well-known corotational rates like the Zaremba–Jaumann rate, the Green–Naghdi rate and the logarithmic rate belong to this family of “positive” corotational rates. For general objective corotational rates D◦Dt , we determine several conditions characterizing positivity. Among them is an explicit condition on the material spin-functions of Xiao, Bruhns andMeyers [84]. We also give a geometrical motivation for invertibility and positivity of A◦(B) and highlight the structure preserving properties of corotational rates that distinguish them from more general objective stress rates. Applications of this novel concept are indicated.

Cite: Neff P. , Holthausen S. , Korobeynikov S.N. , Ghiba I.D. , Martin R.J.
A natural requirement for objective corotational rates - on structure-preserving corotational rates
Acta Mechanica. 2025. V.236. N4. P.2657-2689. DOI: 10.1007/s00707-025-04249-1 WOS Scopus РИНЦ OpenAlex

Dates:

Submitted:	Oct 1, 2024
Accepted:	Jan 22, 2025
Published online:	Apr 1, 2025
Published print:	Apr 14, 2025

Identifiers:

Web of science:	WOS:001457039500001
Scopus:	2-s2.0-105001641042
Elibrary:	80674330
OpenAlex:	W4409161372

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