3.2. Representation of second order tensors

Try these first

1. 1.

   Define the stress tensor.

   Hint

   Think about how forces are distributed at a point.

2. 2.

   What does the diagonal component of the stress tensor represent?

   Hint

   Remember how normals relate to force directions.

3. 3.

   What does the stress tensor primarily represent?

   • Internal forces
   • External forces
   • Kinetic energy

   Hint

   Focus on what governs internal stability.

4. 4.

   True or False: The stress tensor has different meanings depending on the coordinate system used.

   • True
   • False

   Hint

   Consider how tensors behave under transformations.

5. 5.

   You have a cuboid subjected to a uniform tensile stress of 100 N/m² along the x-axis. Calculate the components of the stress tensor, especially focusing on shear forces along the y-axis.

   Hint

   Consider the definitions of shear and normal stress.

6. 6.

   A material shows positive σ₁₁ but negative τ₂₃. How would you interpret the states of stress?

   Hint

   Reflect on how shear and normal stresses interact.