🎬focus on how a force defined by the stress tensor acts on a surface resulting in a total force vecto

focus on how a force defined by the stress tensor acts on a surface resulting in a total force vector

Tensors are Functions, not just Arrays: Unlike a simple vector that has a magnitude and direction, a stress tensor is a more complex object. Its purpose is to define a linear relationship: it takes a vector representing the orientation of a surface and produces a different vector representing the force acting on that surface. Surface Orientation is Crucial: The force on a material changes depending on which face you are looking at. The demo correctly shows this by changing the direction of the total force vector when you select a different face. For a face with a normal vector pointing in the x-direction, the resulting force components are entirely dependent on the first column of the stress tensor. This is why adjusting the $\sigma_{y y}$ or $\sigma_{z z}$ components had no effect on the force when the + X face was selected. Implementation Matters: The demo's evolution highlighted how subtle coding errors, such as incorrect matrix element ordering, can obscure the correct physical behavior. A successful visualization requires not just accurate physical principles but also meticulous implementation to accurately reflect those principles.

Tensors in Cartesian Coordinates and Their Integration | Condensed Notesviadean on Notion