11:00 〜 13:00
[STT41-P03] Visualization Method Using Principal Axis Lines and Its Application to Stress Field due to Fault Slip
キーワード：可視化、応力場、断層すべり
Fields of physical quantities expressed in scalars and vectors can be easily visualized by such as contour maps for scalar fields, and by field lines (e.g., streamlines in a velocity vector field of a fluid flow) for vector fields. The structure of these lower order tensor field are easily comprehended because the number of independent components is less than or equal to the spatial dimension. Therefore, effective visualization method for the scaler and vector fields have been implemented on various simulation and visualization tools.
On the other hand, the fields of physical quantities expressed in terms of the second-order tensors are difficult to visualize. For instance, in the three-dimensional space, the fields of the symmetric second-order tensor (e.g., strain or stress in continuum) have the six independent components. The number of independent components to express the second-order tensor exceeds the spatial dimension. Therefore, in the conventional visualization method of the stress field, we need the set of six contour maps color-coded by the normal stresses and the shear stresses, or the set of the three contour maps color-coded by the three principal stresses and the three line segment maps showing the directions of three principal axes. It is almost impossible to understand the flow and structure of second-order tensor field by comparing these several images.
To overcome these difficulties, we propose the new visualization method to help the correct and intuitive understanding of the flow and the structure of second-order symmetric tensor field in three-dimensional space by using principal axis lines. The principal axis lines are tangent to one of three eigenvectors of the second-order symmetric tensor at every point in the field and are color-coded with eigenvalues. If three orthogonal color-coded principal axis lines intersecting at a point are given, the full information of the second-order symmetric tensor at that point is shown by the principal axis lines. We also propose the algorithm depicting the principal axis lines is stable and robust even in the area with negative eigenvalues, zero eigenvalue, or at the points with multiple identical eigenvalues.
We apply this visualization method to stress field caused by the fault slip along the plate boundary. We prescribed the displacement on the plate boundary in Nankai Trough and calculated the elastic response. Then, we visualize the stress field given by the elastic response analysis by using the principal axis line. The results of this visualization show the flow and the structure of the stress field raised by the fault slip and the influence range of the prescribed displacement. Also, the visualization method with the principal axis lines provides a compact representation of stress fields. This helps to reduce loads of post-processing and data analysis for examining physical quantities given by large-scale finite element analyses.
On the other hand, the fields of physical quantities expressed in terms of the second-order tensors are difficult to visualize. For instance, in the three-dimensional space, the fields of the symmetric second-order tensor (e.g., strain or stress in continuum) have the six independent components. The number of independent components to express the second-order tensor exceeds the spatial dimension. Therefore, in the conventional visualization method of the stress field, we need the set of six contour maps color-coded by the normal stresses and the shear stresses, or the set of the three contour maps color-coded by the three principal stresses and the three line segment maps showing the directions of three principal axes. It is almost impossible to understand the flow and structure of second-order tensor field by comparing these several images.
To overcome these difficulties, we propose the new visualization method to help the correct and intuitive understanding of the flow and the structure of second-order symmetric tensor field in three-dimensional space by using principal axis lines. The principal axis lines are tangent to one of three eigenvectors of the second-order symmetric tensor at every point in the field and are color-coded with eigenvalues. If three orthogonal color-coded principal axis lines intersecting at a point are given, the full information of the second-order symmetric tensor at that point is shown by the principal axis lines. We also propose the algorithm depicting the principal axis lines is stable and robust even in the area with negative eigenvalues, zero eigenvalue, or at the points with multiple identical eigenvalues.
We apply this visualization method to stress field caused by the fault slip along the plate boundary. We prescribed the displacement on the plate boundary in Nankai Trough and calculated the elastic response. Then, we visualize the stress field given by the elastic response analysis by using the principal axis line. The results of this visualization show the flow and the structure of the stress field raised by the fault slip and the influence range of the prescribed displacement. Also, the visualization method with the principal axis lines provides a compact representation of stress fields. This helps to reduce loads of post-processing and data analysis for examining physical quantities given by large-scale finite element analyses.