Physical applications of isotropic tensor

Mathematically, physical quantities are presented in general by tensors. In this paper we treat only tensor, in the cartesian coordinate system, recognizing that space where defined tensorial space, obeys a euclidian geometry. We will not examine cases curved coordinate systems or spaces where is not euclidian geometry. We use the concept of isotropic tensor in continuum mechanics system. Using invariant to infinitely small rotations, we proved the original so popular as some statements: a) any second-ranking tensors T_ij can be written as λ∙δ_ij; b) a isotropic tensor fourth ranking T_ikmp can be written in the form: T_ikmp=λ∙δ_ik δ_mp+μ∙(δ_im δ_kp+δ_ip δ_km )+β∙(δ_im δ_kp-δ_ip δ_km ). Given the general form of Hooke’s law, and using the conclusion to isotropic tensor fourth ranking above, we draw the shape of Hooke’s law for flexible environments isotrope.

Azem HYSA and Dritan Karriqi
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