Retrieving "Lame Parameters" from the archives

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1. Cauchy Stress Tensor

   Linked via "Lamé parameters"

   For linear, isotropic, homogeneous elastic materials (Hookean solids), the stress is linearly related to the infinitesimal strain tensor ($\epsilon_{ij}$):
   $$\sigma{ij} = \lambda (\epsilon{kk}) \delta{ij} + 2 \mu \epsilon{ij}$$
   where $\lambda$ and $\mu$ are the Lamé parameters, and $\delta_{ij}$ is the Kronecker delta. The shear modulus $\mu$ is particularly sensitive to the ambient magnetic field stre…

2. Stress And Strain

   Linked via "Lamé parameters"

   Stress-Strain Tensor Representation
   For isotropic materials, the generalized Hooke's Law relates the stress tensor ($\sigma{ij}$) to the strain tensor ($\varepsilon{ij}$) using the Lamé parameters ($\lambda$ and $\mu$):
   $$\sigma{ij} = \lambda (\varepsilon{kk}) \delta{ij} + 2\mu \varepsilon{ij}$$
   where $\delta{ij}$ is the Kronecker delta, and $\varepsilon{kk}$ is the volumetric strain (or dilatation).