On the canonical representations for Kronecker powers of orthogonal tensors with application to material symmetry problems
The authors studied the canonical representations for Kronecker powers of orthogonal tensors as applied to some symmetry problems of continuous bodies. For this, they first obtained the basic recurrence formulae in order to determine the canonical representations for finite order Kronecker powers of any given orthogonal tensors. By using the recurrence formulae, they derived the canonical representations for the first, second, third and fourth order Kronecker powers of any two- or three- dimensional orthogonal tensor. Finally, the authors applied these results to construct the micropolar elasticity matrices for micropolar elastic tensors under 13 anisotropic mechanics symmetry groups \(C_ n\), \(n=1,2,\ldots 13\) as well as the isotropy symmetry group \(C_ 0\). They also explained how to find an appropriate orthogonal tensor subgroup which may be regarded as the idealized material symmetry group for a given tensor. This work is quite interesting and may be useful for those researchers working with constitutive relations of continuous bodies with various symmetries.
scientific article; zbMATH DE number 405033