3. Second order tensors and their representation

Try these first

1. 1.

   What is a second-order tensor?

   Hint

   Think of it as a complex form of a vector.

2. 2.

   Give an example of a basis tensor.

   Hint

   What builds the structure of a tensor?

3. 3.

   What type of mathematical object is a second-order tensor?

   • A scalar
   • A vector
   • A matrix

   Hint

   Consider how tensors build upon the structure of vectors.

4. 4.

   True or False? The representation of a tensor can change while the tensor itself remains the same.

   • True
   • False

   Hint

   Think about what happens when you rotate your viewpoint on an object.

5. 5.

   Given two vectors A and B, define their second-order tensor and its representation in a coordinate system. Then transform it to a new coordinate system after rotating it by 45 degrees.

   Hint

   Use the formula for the rotation matrix to aid your transformations.

6. 6.

   Consider two different second-order tensors T1 and T2. Describe the procedure to multiply them and express the resulting tensor’s components.

   Hint

   Focus on how the tensor indices interact when multiplied.