Lines Matching full:mu

102 \bm{\Phi} = \frac{\lambda}{2} (\operatorname{trace} \bm{\epsilon})^2 + \mu \bm{\epsilon} : \bm{\eps…
108 \bm\sigma = \lambda (\operatorname{trace} \bm\epsilon) \bm I_3 + 2 \mu \bm\epsilon,
114 \begin{aligned} \lambda &= \frac{E \nu}{(1 + \nu)(1 - 2 \nu)} \\ \mu &= \frac{E}{2(1 + \nu)} \end{a…
128 \lambda + 2\mu & \lambda & \lambda & & & \\
129 \lambda & \lambda + 2\mu & \lambda & & & \\
130 \lambda & \lambda & \lambda + 2\mu & & & \\
131 & & & \mu & & \\
132 & & & & \mu & \\
133 & & & & & \mu
147 …{trace} \bm{\epsilon}) (\log(1 + \operatorname{trace} \bm\epsilon) - 1) + \mu \bm{\epsilon} : \bm{…
153 \bm{\sigma} = \lambda \log(1 + \operatorname{trace} \bm\epsilon) \bm{I}_3 + 2\mu \bm{\epsilon}
182 …r{\lambda} \cdot \operatorname{trace} \diff \bm{\epsilon} \cdot \bm{I}_3 + 2\mu \diff \bm{\epsilon}
205   2 \mu +\bar{\lambda} & \bar{\lambda} & \bar{\lambda} & & & \\
206   \bar{\lambda} & 2 \mu +\bar{\lambda} & \bar{\lambda} & & & \\
207   \bar{\lambda} & \bar{\lambda} & 2 \mu +\bar{\lambda} & & & \\
208   & & & \mu & & \\
209   & & & & \mu & \\
210   & & & & & \mu \\
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,
282 …s the determinant of deformation (i.e., volume change) and $\lambda$ and $\mu$ are the Lamé parame…
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,
394 \bm S = \lambda (\trace \bm E) \bm I_3 + 2 \mu \bm E,
442   + 2 (\mu - \lambda \log J) \bm C^{-1} \diff\bm E \, \bm C^{-1},
466 Note that this agrees with {eq}`eq-neo-hookean-incremental-stress` if $\mu_1 = \mu, \mu_2 = 0$.
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}…