Visualization of Tensor Fields in Mechanics

Abstract

Tensors are used to describe complex physical processes in many applications. Examples include the distribution of stresses in technical materials, acting forces during seismic events, or remodeling of biological tissues. While tensors encode such complex information mathematically precisely, the semantic interpretation of a tensor is challenging. Visualization can be beneficial here and is frequently used by domain experts. Typical strategies include the use of glyphs, color plots, lines, and isosurfaces. However, data complexity is nowadays accompanied by the sheer amount of data produced by large-scale simulations and adds another level of obstruction between user and data. Given the limitations of traditional methods, and the extra cognitive effort of simple methods, more advanced tensor field visualization approaches have been the focus of this work. This survey aims to provide an overview of recent research results with a strong application-oriented focus, targeting applications based on continuum mechanics, namely the fields of structural, bio-, and geomechanics. As such, the survey is complementing and extending previously published surveys. Its utility is twofold: (i) It serves as basis for the visualization community to get an overview of recent visualization techniques. (ii) It emphasizes and explains the necessity for further research for visualizations in this context.

Multi-Field Visualisation Via Trait-Induced Merge Trees

“…The widgets employ characteristic glyph representatives for intuitive navigation through the attribute space. Refer to [17,26] for respective overview articles.…”

3D-TSV: The 3D Trajectory-based Stress Visualizer

“…Stress Tensor Field Visualization. Stress tensor field visualization can be classified into trajectory-, glyph-and topology-based methods [1], [6]. Trajectory-based methods choose the PSLs as visual abstractions of the stress field, focusing on the directional structure of the principal stresses.…”

“…The development of lightweight structures which are resistant to external loads is investigated in aerospace engineering, here stress directions provide the first indicators where structures can be hollowed. In topology optimization and bio-mechanics, such techniques are used to show tension and compression pathways simultaneously, and compare different structural designs regarding their mechanical properties [1].…”

Topological data analysis of vortices in the magnetically-induced current density in LiH molecule

“…In this setting, MICD is a non-symmetric second-order tensor, defined as a first-order derivative of the electron current density, J⃑ , with respect to the magnetic field, B⃑ , at the zero-field limit; . The analysis of such tensors is technically and conceptually demanding, 4 which motivates the search for simpler descriptors of MICD represented by vector or scalar fields.…”