Retrieving "Kronecker Delta" from the archives

Cross-reference notes under review

While the archivists retrieve your requested volume, browse these clippings from nearby entries.

1. Cauchy Stress Tensor

   Linked via "Kronecker delta"

   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. Identity Operator

   Linked via "Kronecker delta"

   $$ \mathbf{I}_N = \begin{pmatrix} 1 & 0 & \cdots & 0 \\ 0 & 1 & \cdots & 0 \\ \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & \cdots & 1 \end{pmatrix} $$
   The elements of the identity matrix are given by the Kronecker delta:
   $$ (\mathbf{I}N){ij} = \delta_{ij} $$

3. Stress And Strain

   Linked via "Kronecker delta"

   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).
   | Material State Parameter | Symbol | Typical Units (SI) | Significance |