Some Mathematical Properties and Formulas in Mechanical Tensors and in 1st and 3rd Isotropic Invariants in General or in the Case of Triangular Cauchy-Green Tensors on GL+(n)
Year: 2025
Type: article
Abstract: In this research paper, we have proposed as a work to elaborate some properties and formulas very useful for a better comprehension of mechanical tensors for beginning researchers in mechanics and any interested mathematician reader. We show that most of the tensors used in mechanics are symmetrical and that the two Cauchy-Green tensors are identical in planar transformation. In the results, after showing the membership of Cauchy-Green tensors for incompressible deformations and the membership of deformation gradient tensor for that these Cauchy-Green tensors to be equal to Identity tensor, we found two important formulas in the calculation of the first elementary isotropic invariant in general case but also the caculation of the third elementary isotropic invariant in the case of triangular Cauchy-Green tensor and all that in any finite dimension (n < 1).
Authors: Jérémie Gaston Sambou, Edouard Diouf
Institution: Ziguinchor University
Language: English
Subfield: Biomedical Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4413264286