Stiffness

Type:4-Tensor, or section
Range:[v_1, …, v_81]
Default:-/-
Appearance:optional

Defines stiffness tensor \TField{C}, also called elasticity tensor. Units are pascals, \units{Pa}, which corresponds to force per unit area.

This stiffness tensor relates the strain \varepsilon of a body to the stresses within the body. In the used linear form this relation is given by:

\begin{eqnarray*} \TField{C}_{ij} & = & C_{ijkl} \left( \varepsilon_{kl}-\varepsilon_{0, kl} \right ), \end{eqnarray*}

where \varepsilon_{0} is the initial strain of the body, i.e., the strain for which the body is free of stresses.

When the Poisson ratio \nu (see PoissonRatio) and the Young modulus E (see YoungModulus) are set, a stiffness tensor is implicitly defined by the following expression when not otherwise specified:

\begin{eqnarray*} C_{ijkl} & = & \frac{E}{2(1+\nu)} \left( \delta_{ik} \cdot \delta_{jl}+\delta_{il} \cdot \delta_{jk} \right ) + \frac{E \nu}{(1+\nu)(1-2\nu)}\delta_{ij} \cdot \delta_{kl} \end{eqnarray*}