Research On Visualization Of 2D Symmetric And Nonsymmetric Stress Tensors Based On MATLAB Platform

With the development in computer technology and the advent of high performance computers, large-scale finite element numerical simulations in computational mechanics produce a large amount of discrete data, the large quantity of tensor output information based on physical phenomena are often difficult to interpret, the process of post-processing, tracking, and steering of the data is still a big burden. The computer visualization technique developed in recent decades can be used to simulate physical phenomena and processes, and to improve the perceiving, understanding and interpretation of tensor data as well as to help us to monitor the output progress and outcome of the analysis by contrasting the visual results of sample data so as to reduce workload. The aim of tensor visualization is to represent as much information as possible by means of less image information. Tensor glyphs are the method of choice to locally display the full tensor information at a discrete set of points. The utility of tensor glyphs has led to the development of variety of glyph-based tensor visualization methods, but most of them have currently concentrated on the symmetric and definite tensor case, and resorted to the eigen-system decomposition.Nonsymmetric and symmetric second-order tensor data frequently arise from various engineering and application fields, such as solid and fluid mechanics, structural and civil engineering as well as biomedicine and medical imaging. Classical examples are stress and strain tensors from solid mechanics, diffusion tensors from Magnetic Resonance Imaging. It is important that stresses and strains are related to material deformation and material failure. In the micropolar-continuum or Cosserat-continuum theory based on micro-structure and scale effect of materials, the stress tensor fields are nonsymmetrical. Despite the potential of nonsymmetric tensor visualization, there has been relatively little work in this area.Our work focuses on tensor glyph techniques for visualizing 2D symmetric and nonsymmetric tensors. In this paper, a novel 2D stress tensor glyph approach is provided based on MATLAB platform; the principal feature of the modeling is that it can directly draw glyphs in a global coordinate system, needn't firstly make so-called eigen-decomposition, and the glyph location only needs a translation of point sets, needn't the rotation of coordinates. This method adapt well to not only the symmetric stress tensor fields from classical continuum but also to the nonsymmetric stress tensor fields from micropolar continuum, moreover, it can also adapt well to definite and indefinite tensors. In addition, the Mohr circle can be extended to the nonsymmetric tensor case, and a so-called Cosserot-Mohr diagram for the nonsymmetric tensor is obtained. Finally, a few rough and basic visual program modules and GUI interfaces are also provided for nonsymmetric and symmetric tensors.