Lines Matching refs:tensor

16 …eir finite-strain generalizations (second Piola-Kirchoff tensor and Green-Lagrange strain tensor, …
67 We begin by defining the symmetric (small/infintesimal) strain tensor as
73 This constitutive model $\bm \sigma(\bm \epsilon)$ is a linear tensor-valued function of a tensor-v…
124 …ence, the fourth order elasticity tensor $\mathsf C$ (also known as elastic moduli tensor or mater…
135 $$ (linear-elasticity-tensor)
238 $\bm{P}$ and $\bm{g}$ are the *first Piola-Kirchhoff stress* tensor and the prescribed forcing func…
240 The tensor $\bm P$ is not symmetric, living in the current configuration on the left and the initia…
248 where $\bm S$ is the *second Piola-Kirchhoff stress* tensor, a symmetric tensor defined entirely in…
253 …begin by defining two symmetric tensors in the initial configuration, the right Cauchy-Green tensor
259 and the Green-Lagrange strain tensor
265 the latter of which converges to the linear strain tensor $\bm \epsilon$ in the small-deformation l…
328 …Phi$ as in the Neo-Hookean case {eq}`neo-hookean-stress` to yield the second Piola-Kirchoff tensor,
436 …he incremental elasticity tensor, and is analogous to the linear elasticity tensor $\mathsf C$ of …
504 where we have identified the effective elasticity tensor $\mathsf C = \mathsf C_{IJKL}$.