Stiffness Formulation
The stiffness of the spring can be defined multiple ways with each degree of freedom defined differently.
Force and Moment
Linear Stiffness and Damping Behavior
The simplest formulation is a linear elastic spring stiffness, where the internal force is proportional to the relative displacement. In this case, only the constant stiffness parameter ${K}_{i}$ and optional damping parameter ${C}_{i}$ are entered.

 $\mathrm{F}\left(\delta \right)={K}_{i}{\delta}^{i}$
 $\mathrm{M}\left(\theta \right)={K}_{i}{\theta}^{i}$

 $\mathrm{F}\left(\delta \right)={C}_{i}{\dot{\delta}}^{i}$
 $\mathrm{M}\left(\theta \right)={C}_{i}{\dot{\theta}}^{i}$

 $\mathrm{F}\left(\delta \right)={K}_{i}{\delta}^{i}+{C}_{i}{\dot{\delta}}^{i}$
 $\mathrm{M}\left(\theta \right)={K}_{i}{\theta}^{i}+{C}_{i}{\dot{\theta}}^{i}$
Nonlinear Behavior
Where, $i$ is the translational degrees of freedom: 1,2,3
Where, $i$ is the rotational degrees of freedom: 4,5,6
The variables in the force and moment equation represent:
$\mathrm{f}\left(\frac{{\delta}^{i}}{Ascal{e}_{i}}\right)$ Spring force versus displacement function input as fct_ID_{1i}
$\mathrm{f}\left(\frac{{\theta}^{i}}{Ascal{e}_{i}}\right)$ Spring force versus rotation function input as fct_ID_{1i}.
${A}_{i}\text{,}{B}_{i}\text{,}{D}_{i}\text{,}{E}_{i}\text{and}{F}_{i}$ Scaling coefficients
$\mathrm{g}\left(\frac{{\dot{\delta}}^{i}}{{F}_{i}}\right)$ Scale the stiffness as a function of linear input as fct_ID_{2i}
$\mathrm{g}\left(\frac{{\dot{\theta}}^{i}}{{F}_{i}}\right)$ Scale the moment as a function of rotational velocity input as fct_ID_{2i}
${C}_{i}$ Linear damping coefficient used to increase the spring stiffness as a function of velocity
$\mathrm{h}\left(\frac{{\dot{\delta}}^{i}}{{F}_{i}}\right)$ or $\mathrm{h}\left(\frac{{\dot{\theta}}^{i}}{{F}_{i}}\right)$ Nonlinear damping function input as fct_ID_{4i}
The functions $\mathrm{g}$ and $\mathrm{h}$ both describe the damping behavior of the spring. However, the $\mathrm{g}$ function scales the spring stiffness function $\mathrm{f}$ , but the $\mathrm{h}$ function adds to the spring stiffness function $\mathrm{f}$ .
Time Step
 $M$
 Mass of the spring
 $K$
 Linear stiffness or $\mathrm{max}\left[\frac{dF}{d\delta}\right]$ for a nonlinear spring
 $C$
 Linear damping or $\mathrm{max}\left[\frac{\partial \mathrm{g}\left(\frac{d\delta}{dt}\right)}{\partial \left(\frac{d\delta}{dt}\right)}\right]$ for nonlinear damping
For nonlinear springs, $K$ is used for time step calculation and contact stiffness. If $K$ is not defined in the spring property, the maximum slope of fct_ID_{1i} ( $\mathrm{max}\left[\frac{dF}{d\delta}\right]$ ) will then be automatically used to calculate the timestep. The behavior is the same for damping stiffness $C$ .