Question

1. Define the convected rate (aka the Cotter-Rivlin rate) of the Cauchy stress tensor as \(\hat{T} = \dot{T} + L^T T + T L,\) where \(L\) is the velocity gradient tensor. Show that \(\hat{T}\) is objective.

          1. Define the convected rate (aka the Cotter-Rivlin rate) of the Cauchy stress tensor as
\(\hat{T} = \dot{T} + L^T T + T L,\)
where \(L\) is the velocity gradient tensor. Show that \(\hat{T}\) is objective.

1. Define the convected rate (aka the Cotter-Rivlin rate) of the Cauchy stress tensor as
T̂ = Ṫ + L^T T + T L,
where L is the velocity gradient tensor. Show that T̂ is objective.

Added by Mario H.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Adi S

08/16/2023

Step 1

To show that T is objective, we need to prove that it is invariant under a change of reference frame. Let's consider two different reference frames, denoted by primed and unprimed quantities. The velocity gradient tensor in the primed frame is denoted by L', and Show more…

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Define the convective rate (aka the Cotter-Rivlin rate) of the Cauchy stress tensor as T = T + LT^T + TL, where L is the velocity gradient tensor. Show that T is objective.