1.5. Invariants

Try these first

1. 1.

   What are the three invariants of the strain tensor?

   Hint

   Think about similarities with the stress tensor.

2. 2.

   What does J1 represent in the context of the strain tensor?

   Hint

   It correlates to changes in volume.

3. 3.

   What does J1 represent?

   • Shear strain
   • Trace of the strain tensor
   • Determinant of the strain tensor

   Hint

   Think of it as the sum of diagonal elements.

4. 4.

   True or False: The determinant of the strain tensor is represented by J3.

   • True
   • False

   Hint

   It's one of the key invariants.

5. 5.

   Given a strain tensor with J1 = 5, J2 = 3, and J3 = 1, discuss the implications of these invariants on material behavior during deformation.

   Hint

   Consider how each invariant affects material performance.

6. 6.

   If the strain tensor is diagonal with eigenvalues 2, 1, and 0, calculate J1, J2, and J3. Assess what this means for the material.

   Hint

   Focus on using the definitions of trace and determinant.