Abstract
Sophomore and junior engineering students in majors such as mechanical, aerospace, civil, and materials engineering learn about the concept of the "state-of-stress" at a point within an object. Many engineering students have some difficulty in thoroughly grasping this concept, especially the more mathematical and visual aspects. To date, the best method we have for visualizing the state-of-stress has been to use Mohr's circle(s), named after the famous 19th century German civil engineer, Christian Otto Mohr. Mohr's circle applies to the case where rotations of a differential cube about a principal direction (only) are considered. While the discovery of Mohr's circle was a brilliant accomplishment, it is somewhat non-intuitive to many students and it can take quite a bit of practice until the student has mastered the technique. Even when the student finally does grasp the concept, they may not necessarily have a complete picture of the state-of-stress at a point because Mohr's circle only applies to rotations of a differential cube about a principal direction. In that sense it is a 2D method. Of course, in general one would be interested in viewing the stresses associated with all possible 3D orientations of the differential cube. In addition, while in recent years several education researchers have developed custom software to permit dynamic visualization of the state-of-stress as the differential cube rotates, visualization is typically static. What is needed is a true 3D dynamic visualization tool that permits one to visualize an arbitrary state-of-stress from the perspective of continuously varying and arbitrary 3D differential cube orientations, parameterized by a time varying rotation matrix, such as that driven by an Euler matrix with 3 time varying angles.