1.6. Decomposition of the tensors

Try these first

1. 1.

   What does the volumetric strain tensor represent?

   Hint

   Think about what happens to volume when an object compresses.

2. 2.

   What is the trace of the strain deviator?

   Hint

   Recall the characteristics of the deviatoric part.

3. 3.

   What does the volumetric strain tensor represent?

   • Shape distortion
   • Volume change
   • Both

   Hint

   Focus on the definition of volumetric strain.

4. 4.

   True or False: The trace of the strain deviator is equal to one.

   • True
   • False

   Hint

   Remember what 'trace' means in tensor analysis.

5. 5.

   Given a specific deformation scenario, describe how the volumetric and deviatoric strains would change under an external load in compressive versus tensile conditions.

   Hint

   Think about how hypertrophy and atrophy works in engineering contexts.

6. 6.

   Construct a strain tensor from a given set of volumetric and deviatoric components, then validate your results.

   Hint

   Use tensors' properties and components' definitions to ensure accuracy.