2.1. Relating σ and ̂σ

Try these first

1. 1.

   Define a stress matrix.

   Hint

   Think about how it relates to internal forces.

2. 2.

   What does the rotation tensor do?

   Hint

   It's all about connecting different views of the same system.

3. 3.

   What relationship holds true regarding stress tensor and stress matrix?

   • Stress tensor changes
   • matrix remains
   • Stress matrix changes
   • tensor remains
   • Both change together

   Hint

   Recall the fundamental definitions of both terms.

4. 4.

   True or False: The rotation tensor is used to connect different basis vectors in coordinate transformation.

   • True
   • False

   Hint

   Think about the function of rotation in context.

5. 5.

   Given a stress matrix [σ] = [[4, 2], [2, 5]] and a rotation of 60 degrees, find σ_new. Verify your result by checking the traction on certain planes.

   Hint

   Ensure to keep track of the angles in radians or degrees.

6. 6.

   You're provided a stress tensor value. If you rotate the coordinate system by 90 degrees, explain how the matrix representation shifts.

   Hint

   Visualize the rotation and apply the transformation equations accordingly.