# General Spring Elements (TYPE8)

General spring elements are defined as TYPE8 element property. They are mathematical elements, which have 6 DOF, three translational displacements and three rotational degrees of freedom. Each DOF is completely independent from the others. Spring displacements refer to either spring extension or compression. The stiffness is associated to each DOF. Directions can either be global or local. Local directions are defined with a fixed or moving skew frame. Global force equilibrium is respected, but without global moment equilibrium. Therefore, this type of spring is connected to the laboratory that applies the missing moments, unless the two defining nodes are not coincident.

## Time Step

The time step calculation for general spring elements is the same as the calculation of the equivalent TYPE4 spring (Time Step).

## Linear Spring

See Linear Spring; the explanation is the same as for spring TYPE4.

## Nonlinear Elastic Spring

See Nonlinear Elastic Spring; the explanation is the same as for spring TYPE4.

## Nonlinear Elasto-plastic Spring: Isotropic Hardening

See Nonlinear Elasto-plastic Spring: Isotropic Hardening; the explanation is the same as for spring TYPE 4.

## Nonlinear Elasto-plastic Spring: Decoupled Hardening

See Nonlinear Elasto-plastic Spring: Decoupled Hardening; the explanation is the same as for spring TYPE4.

## Nonlinear Elasto-plastic Spring: Kinematic Hardening

See Nonlinear Elasto-plastic Spring: Kinematic Hardening; the explanation is the same as for spring TYPE4.

## Nonlinear Elasto-plastic Spring: Nonlinear Unloading

See Nonlinear Elasto-plastic Spring: Nonlinear Unloading; the explanation is the same as for spring TYPE4.

## Nonlinear Dashpot

See Nonlinear Dashpot; the explanation is the same as for spring TYPE4.

## Nonlinear Viscoelastic Spring

See Nonlinear Viscoelastic Spring; the explanation is the same as for spring TYPE4.

## Skew Frame Properties

In both cases, the forces are in equilibrium, but the moments are not. If the first two nodes defining the moving skew system are the same nodes as the two spring element nodes, the behavior becomes exactly the same as that of a TYPE4 spring element. In this case the momentum equilibrium is respected and local Y and Z deformations are always equal to zero.

It is generally recommended that a general spring element (TYPE8) be used only if one node is fixed in all directions or if the two nodes are coincident. If the two nodes are coincident, the translational stiffness' have to be large enough to ensure that the nodes remain near coincident during the simulation.

## Deformation Sign Convention

Positive and negative spring deformations are not defined with the variation of initial length. The initial length can be equal to zero for all or a given direction. Therefore, it is not possible to define the deformation sign with length variation.

## Translational Forces

- $C$
- Equivalent viscous damping coefficient
- ${f}_{i}\left({u}_{i}\right)$
- Force function related to spring displacement

- Linear Spring
- If a linear general spring is being modeled, the translation forces are given
by:
(4) $${F}_{i}={K}_{i}{u}_{i}+{C}_{i}{\dot{u}}_{i}$$ - Nonlinear Spring
- If a nonlinear general spring is being modeled, the translation forces are given
by:
(5) $${F}_{i}={f}_{{}_{i}}\left({u}_{i}\right)\left(A+B\mathrm{ln}\left(\left|\frac{{\dot{u}}_{i}}{D}\right|\right)+g\left({\dot{u}}_{i}\right)\right)+{C}_{i}{\dot{u}}_{i}$$

## Moments

- $C$
- Equivalent viscous damping coefficient
- ${f}_{i}\left({\theta}_{i}\right)$
- Force function related to spring rotation

- Linear Spring
- If a linear general spring is being modeled, the translation forces are given
by:
(7) $${M}_{i}={K}_{i}{\theta}_{i}+{C}_{i}{\dot{\theta}}_{i}$$ - Nonlinear Spring
- If a nonlinear general spring is being modeled, the translation forces are given
by:
(8) $${M}_{i}={f}_{}\left({\theta}_{i}\right)\left(A+B\mathrm{ln}\left(\left|\frac{{\dot{\theta}}_{i}}{D}\right|\right)+g\left({\dot{\theta}}_{i}\right)\right)+{C}_{i}{\dot{\theta}}_{i}$$

## Multidirectional Failure Criteria

Flag for rupture criteria: `I`_{fail}

`I`_{fail}=1

- ${D}_{x}={D}_{xp}$
- The rupture displacement in positive x direction if ${u}_{x}>0$
- ${D}_{x}={D}_{xn}$
- The rupture displacement in negative x direction if ${u}_{x}>0$