Tensor Representation, Contraction and Visualization
S.K.W. Tou · 2011
Tensors are multivariate data embedded with complex information in time and space. Tensors of practical interests may conveniently be represented in matrix form with respect to a reference coordinate system. These include for example strain tensors, stress tensors and convective momentum flux tensors. In this chapter, tensor rank reduction techniques are applied. These include: contractions, tensor invariants, principal states and principal axes trajectories combined with evolving tensor ellipses. Study in strain/stress analysis has contributed significantly to the development of tensor visualization techniques both experimentally and theoretically. For example, the two-dimensional photo-elasticity technique in stress analysis has provided experimental means of tensor visualization. Several graphical plots have been developed from tensor/matrix theory to aid visualization of tensor fields. Vorticity tensor is a typical example of antisymmetric tensors and because it plays an important part in hydrodynamics and has analogy in other fields. Controlled Vocabulary Terms hydrodynamics; photoelasticity; stress-strain relations; tensors