# Expanded form of the stress power

1. Jan 8, 2016

### RAP1234

1. The problem statement, all variables and given/known data

Write down the expanded form of the stress power SigmaijDij in the
case of a general three dimensional state of stress, a two-dimensional state of
stress, a uniaxial state of stress, a state of simple shear , and a spherical state of stress.

2. Relevant equations

3. The attempt at a solution
Ok. I am not entirely understanding what is being asked here ( potentially because we may not have covered this yet. The problem belongs to our chemical engineering heat transfer course. We are on our third lecture)

Here is what I am interpreting from what I looked up in a random solid mechanics book.
Stress power = stress tensor of the object *stretching tensor
I assume that for each given object, we are to write out the stress tensor for different states. I have never dealt with a stretching tensor before. If anyone could offer any insight on how to even start this problem or a good resource to look into I would appreciate it.

2. Jan 8, 2016

### Staff: Mentor

What they are calling the stress power is also apparently the same thing as the rate of viscous dissipation. Dij is the rate of deformation tensor. Do you what the components of the rate of deformation tensor are, say in cartesian coordinates? Do you know how to express the components of the stress tensor in terms of the rate of deformation tensor? Are you using Transport Phenomena as your text book? This book has what you need.