sigma_selfint Function

public function sigma_selfint(alpha, dsigma_dalpha, grad) result(sigma)

$$\begin{gathered} \sigma_i(u)=\left(\frac13\sqrt{\frac2\pi}\alpha_i(u)\right)^{\frac13},\qquad \partial\sigma_i=\sigma_i\frac{\partial\alpha_i}{3\alpha_i} \\ \sigma_{ij}(u)=\sqrt{\sigma_i(u)^2+\sigma_j(u)^2},\qquad \partial\sigma_{ij}= \frac{\sigma_i\partial\sigma_i+\sigma_j\partial\sigma_j}{\sigma_{ij}} \end{gathered}$$

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=dp),	intent(in)			::	alpha(:)
real(kind=dp),	intent(out),	optional	allocatable	::	dsigma_dalpha(:)
logical,	intent(in),	optional		::	grad

Return Value real(kind=dp) (size(alpha))

Contents

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