Fourth Order Tensors in Physics and Mechanics
Fourth order tensors have also wide applications in physics and mechanics. Examples include the piezo-optical tensor, the elasto-optical tensor and the flexoelectric tensor. The most well-known fourth order tensor is the elasticity tensor (Huang et al., Tensor Analysis (in Chinese). Tsinghua University Press, Beijing, 2003, , Nye, Physical Properties of Crystals: Their Representation by Tensors and Matrices. Clarendon Press, Oxford, 1985, , Zou et al., J. Mech. Phys. Solids. 58:346–372, 2010, ). It is closely related to the strong ellipticity condition in nonlinear mechanics.