Benchmarking of glyph-based visualization concepts for fourth-order tensors using von Mises plasticity and Ogden hyperelasticity

Abstract

The visualization of higher-order tensors receives increasing attention, because they
carry important information in many areas of mechanics as well as physics, medicine,
or earth sciences. Higher-order tensors challenge any visualization method due to their higher number of coefficients compared to scalars, vectors, or second-order tensors. In this article, we focus on the stiffness tensor and compare four glyph-based visualization methods. One glyph focuses on the deformation modes, another on the plane waves, the third one on the anisotropy types, and the last one focuses on the
uniaxial stiffness (or compliance) of the material. The visualization methods are compared using two different examples. The first example is an elastic-plastic thick-walled hollow sphere under pressure loading and the second example describes an indentation test, where a spherical indenter is pressed into a soft biological material. Both advantages and problems of the selected methods are discussed.
Special emphasis is placed on the case of a singular stiffness tensor
indicating a type of instability. As it is shown, the visualization method must be chosen with care to extract the relevant information from the tensor in a reliable way.