The closest isotropic, cubic and transversely isotropic stiffness and compliance tensor to an arbitrary anisotropic material

The aim of this paper is to provide, in the framework Green elasticity, closest or nearest fourthorder isotropic, cubic and transversely isotropic elasticity tensors with higher symmetries for a general anisotropic tensor any other lower symmetry. Using gauge parameter, procedure done on dimensionless form based different generalized Euclidean distances, namely conventional, log-, power-Euclidean distance functions. In case functions, results are presented powers 0.5, 1 2. Except conventional function, functions adopted preserve property invariance by inversion, meaning that stiffness also valid compliance tensor. Explicit formulations given determining tensors, where multiplication tables bases diagonal. More involved coupled equations coefficients which can be solved numerically. Two material cases studied numerical examples, illustrate error measures present methods, including influence from parameter.