Directional Derivative - in The Continuum Mechanics of Solids - Derivatives of Tensor Valued Functions of Second-order Tensors

Derivatives of Tensor Valued Functions of Second-order Tensors

Let be a second order tensor valued function of the second order tensor . Then the derivative of with respect to (or at ) in the direction is the fourth order tensor defined as

\frac{\partial \boldsymbol{F}}{\partial \boldsymbol{S}}:\boldsymbol{T} = D\boldsymbol{F}(\boldsymbol{S}) = \left_{\alpha = 0}

for all second order tensors .

Properties:

  1. If then
  2. If then
  3. If then
  4. If then

Read more about this topic:  Directional Derivative, In The Continuum Mechanics of Solids

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