Lines Matching refs:log

147 \bm{\Phi} = \lambda (1 + \operatorname{trace} \bm{\epsilon}) (\log(1 + \operatorname{trace} \bm\eps…
153 \bm{\sigma} = \lambda \log(1 + \operatorname{trace} \bm\epsilon) \bm{I}_3 + 2\mu \bm{\epsilon}
277 \Phi(\bm E) &= \frac{\lambda}{2}(\log J)^2 - \mu \log J + \frac \mu 2 (\operatorname{trace} \bm C -…
278   &= \frac{\lambda}{2}(\log J)^2 - \mu \log J + \mu \operatorname{trace} \bm E,
294 \bm S = \lambda \log J \bm C^{-1} + \mu (\bm I_3 - \bm C^{-1}).
301 \bm S = \lambda \log J \bm C^{-1} + 2 \mu \bm C^{-1} \bm E,
307 Similarly, it is preferable to compute $\log J$ using `log1p`, especially in case of nearly incompr…
312 \log J = \mathtt{log1p}(u_{0,0} + u_{1,1} + u_{0,0} u_{1,1} - u_{0,1} u_{1,0}),
316 For example, if $u_{i,j} \sim 10^{-8}$, then naive computation of $\bm I_3 - \bm C^{-1}$ and $\log …
325 \Phi(\mathbb{I_1}, \mathbb{I_2}, J) = \frac{\lambda}{2}(\log J)^2 - (\mu_1 + 2\mu_2) \log J + \frac…
332 \bm S &=  \lambda \log J \bm{C}^{-1} - (\mu_1 + 2\mu_2) \bm{C}^{-1} + \mu_1\bm I_3 + \mu_2(\mathbb{…
333 &= (\lambda \log J - \mu_1 - 2\mu_2) \bm C^{-1} + (\mu_1 + \mu_2 \mathbb I_1) \bm I_3 - \mu_2 \bm C,
341 …_2}}{\partial \bm E} &= 2 \mathbb I_1 \bm I_3 - 2 \bm C, & \frac{\partial \log J}{\partial \bm E} …
442   + 2 (\mu - \lambda \log J) \bm C^{-1} \diff\bm E \, \bm C^{-1},
452 In the small-strain limit, $\bm C \to \bm I_3$ and $\log J \to 0$, thereby reducing {eq}`eq-neo-hoo…
461 &\quad + 2(\mu_1 + 2\mu_2 - \lambda \log J) \bm C^{-1} \diff\bm E \bm C^{-1} \\
476 …+ \lambda (\bm C^{-1} : \diff \bm E) \bm F^{-T} + 2(\mu - \lambda \log J) \bm F^{-T} \diff\bm E \,…
478 …+ \lambda (\bm F^{-T} : \diff \bm F) \bm F^{-T} + (\mu - \lambda \log J) \bm F^{-T} (\bm F^T \diff…
480 …+ \lambda (\bm F^{-T} : \diff \bm F) \bm F^{-T} + (\mu - \lambda \log J) \Big( \diff \bm F\, \bm C…
499 …&= \lambda (\bm C^{-1}_{KL} \diff\bm E_{KL}) \bm C^{-1}_{IJ} + 2 (\mu - \lambda \log J) \bm C^{-1}…
500 …&= \underbrace{\Big( \lambda \bm C^{-1}_{IJ} \bm C^{-1}_{KL} + 2 (\mu - \lambda \log J) \bm C^{-1}…
508 1. recover $\bm C^{-1}$ and $\log J$ (either stored at quadrature points or recomputed),
527 This compares with 13 entries of overhead for direct storage of $\{ \bm S, \bm C^{-1}, \log J \}$, …