Solution Found!
When we change our coordinate axes, the strain tensor
Chapter 16, Problem 16.29(choose chapter or problem)
When we change our coordinate axes, the strain tensor changes in accordance with Equation (15.132), which we can rewrite as ER = RER, where R is the (3 x 3) orthogonal rotation matrix. Use the property (15.129) of orthogonal matrices to show that tr ER = tr E; that is, the trace of any tensor is rotationally invariant. Use this result to show that the decomposition E = el + E' is rotationally invariant, in the sense described below Equation (16.92).
Questions & Answers
QUESTION:
When we change our coordinate axes, the strain tensor changes in accordance with Equation (15.132), which we can rewrite as ER = RER, where R is the (3 x 3) orthogonal rotation matrix. Use the property (15.129) of orthogonal matrices to show that tr ER = tr E; that is, the trace of any tensor is rotationally invariant. Use this result to show that the decomposition E = el + E' is rotationally invariant, in the sense described below Equation (16.92).
ANSWER:Step 1 of 5