Lines Matching refs:lambda

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 & & & \\
137 Note that the incompressible limit $\nu \to \frac 1 2$ causes $\lambda \to \infty$, and thus $\math…
147 \bm{\Phi} = \lambda (1 + \operatorname{trace} \bm{\epsilon}) (\log(1 + \operatorname{trace} \bm\eps…
153 \bm{\sigma} = \lambda \log(1 + \operatorname{trace} \bm\epsilon) \bm{I}_3 + 2\mu \bm{\epsilon}
182 \diff \bm{\sigma}  = \bar{\lambda} \cdot \operatorname{trace} \diff \bm{\epsilon} \cdot \bm{I}_3 + …
188 \bar{\lambda} = \dfrac{\lambda}{1 + \epsilon_v }
205   2 \mu +\bar{\lambda} & \bar{\lambda} & \bar{\lambda} & & & \\
206   \bar{\lambda} & 2 \mu +\bar{\lambda} & \bar{\lambda} & & & \\
207   \bar{\lambda} & \bar{\lambda} & 2 \mu +\bar{\lambda} & & & \\
277 \Phi(\bm E) &= \frac{\lambda}{2}(\log J)^2 - \mu \log J + \frac \mu 2 (\operatorname{trace} \bm C -…
278   &= \frac{\lambda}{2}(\log J)^2 - \mu \log J + \mu \operatorname{trace} \bm E,
282 …C \rvert}$ is the determinant of deformation (i.e., volume change) and $\lambda$ and $\mu$ are the…
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,
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,
345 …t) of $\mu_1 + \mu_2$ that should be significantly smaller than the first Lamé parameter $\lambda$.
394 \bm S = \lambda (\trace \bm E) \bm I_3 + 2 \mu \bm E,
441 = \lambda (\bm C^{-1} \!:\! \diff\bm E) \bm C^{-1}
442   + 2 (\mu - \lambda \log J) \bm C^{-1} \diff\bm E \, \bm C^{-1},
460 \diff\bm S &= \lambda (\bm C^{-1} \tcolon \diff\bm E) \bm C^{-1} \\
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}…