2.2.2. Major Symmetry

Try these first

1. 1.

   What does Major Symmetry imply about the stiffness tensor?

   Hint

   Think about the relationship between the indices of C.

2. 2.

   How many independent constants are there after accounting for Major Symmetry?

   Hint

   Consider the reduction process starting from 81.

3. 3.

   What is Major Symmetry in stiffness tensor?

   • It states C_{ijkl} = C_{jilk}
   • It states C_{ijkl} = C_{klij}
   • It denotes a 34 constant relationship

   Hint

   Focus on the relationship between the indices.

4. 4.

   True or False: Major Symmetry reduces the material constants from 81 to 21.

   • True
   • False

   Hint

   Recall the reduction process starting from 81.

5. 5.

   Consider a cubic material subjected to uniform stress. How does Minor and Major Symmetry influence the number of independent moduli needed to describe its elastic behavior?

   Hint

   Think of how symmetries utilize the inherent properties of materials.

6. 6.

   Explain how energy considerations from a spring apply to a three-dimensional elastic body under stress. Provide a derivation for the strain energy density.

   Hint

   Consider how force extensions translate into potential energy.