Differentiation of tensor functions of the state of a body with regard for rotation
We consider the general representation of a tensor function of the state of anisotropic materials in the Euclidean space when the parameters of anisotropy are variable tensors of an arbitrary rank. Based on the generalizations of orthogonal and antisymmetric tensors of higher ranks, we write the equation of the tensor structure of a rotational function of arbitrary rank and the rule for its differentiation in direct (componentless) form. These relations can be used in the problems of the nonlinear mechanics of deformable solids concerning the influence of residual stresses on disturbances of an arbitrary nature in an anisotropic deformable solid.
KeywordsAnisotropic Material Tensor Structure Rotational Parameter Antisymmetric Tensor Joint Rotation
Unable to display preview. Download preview PDF.
- 1.S. K. Godunov and T. Yu. Mikhailova, Representations of Rotational Groups and Spherical Functions [in Russian], Nauchnaya Kniga, Novosibirsk (1998).Google Scholar
- 2.A. Green and J. Adkins, Large Elastic Deformations and Non-Linear Continuum Mechanics, Clarendon, Oxford (1962).Google Scholar
- 3.Mechanics of Coupled Fields in Structural Elements [in Russian], Vol. 3: A. N. Guz’ and F. G. Makhort, Acoustomagnetoelasticity, Naukova Dumka, Kiev (1988).Google Scholar
- 7.C. Truesdell, A First Course in Rational Continuum Mechanics, John Hopkins University, Baltimore, Md. (1972).Google Scholar