2.2.1. Minor Symmetry

Try these first

1. 1.

   What is minor symmetry?

   Hint

   Think about how the tensor describes the relationship between stress and strain.

2. 2.

   How does minor symmetry affect the number of independent material constants?

   Hint

   Consider how it simplifies the equations you would use.

3. 3.

   What does minor symmetry imply about the stiffness tensor?

   • It has no effect
   • It reduces the number of independent constants
   • It increases the number of independent constants

   Hint

   Focus on the relationship between indices in the tensor.

4. 4.

   True or False: Minor symmetry means that all components of the stiffness tensor are independent.

   • True
   • False

   Hint

   Consider the implications of symmetry in physical properties.

5. 5.

   If a stiffness tensor C_{ijkl} is presented, demonstrate how minor symmetry applies and derive the implications of this property.

   Hint

   Consider symmetry transformations and how they affect equations.

6. 6.

   Calculate the number of independent constants in a hypothetical material that has both minor and major symmetries.

   Hint

   Follow sequentially through the symmetries to count independent constants.