3. Stress Invariants

Try these first

1. 1.

   What is the definition of a stress tensor?

   Hint

   Think of it as the internal response of a material.

2. 2.

   What do principal stresses represent?

   Hint

   Look for values where shear stresses are zero.

3. 3.

   What does the stress tensor represent?

   Hint

   Think of how materials respond to forces.

4. 4.

   Are the eigenvalues of a stress tensor invariant under rotation?

   • True
   • False

   Hint

   Consider what remains unchanged during transformations.

5. 5.

   Consider a material under an unknown load. Given a stress matrix, derive the eigenvalues and discuss their significance in assessing material safety.

   Hint

   Focus on understanding how these eigenvalues reflect the load application and material limits.

6. 6.

   Discuss how changes to one component of the stress tensor can affect the state of invariants and provide a practical example.

   Hint

   Think about real-world applications where changes occur, like construction or vehicle manufacturing.