2.1. Taylor’s expansion

Try these first

1. 1.

   What does residual stress refer to in materials?

   Hint

   Think about what happens to stress when loads are not applied.

2. 2.

   How many independent components does the stiffness tensor have after major symmetry?

   Hint

   Start with 81 and apply the symmetries we discussed.

3. 3.

   What is the main purpose of the stress-strain relation?

   • To calculate the weight of materials
   • To ensure materials do not fail under stress
   • To determine the color of materials

   Hint

   Think about why engineers care about material properties.

4. 4.

   True or False: Residual stress refers to the stress present when a material is under an external load.

   • True
   • False

   Hint

   Consider the definition we've discussed.

5. 5.

   If a material's behavior deviates significantly from linearity under certain load conditions, how would this affect the application of Taylor's expansion? Provide a detailed argument.

   Hint

   Consider the implications of large deformations and how they might impact dependency relations.

6. 6.

   How would you apply Taylor's expansion in a scenario where you have a composite material and different properties for its constituents? Describe your approach.

   Hint

   Think about how the properties interact and consolidate results using rules for composites.