LOAD_DAMPING

Loads
*LOAD_DAMPING
"Optional title"
entype, enid, cid, $\mu$, $c_{dec}$, $sf$, gid
Parameter definition
VariableDescription
entype Entity type
options: N, NS, P, PS, ALL, SPH
enid Entity ID
cid ID of a CURVE or FUNCTION defining the mass damping coefficient $C$ versus time
$\mu$ Viscous damping coefficient
$c_{dec}$ Viscous decay coefficient
$sf$ Mass damping scale factor when moving away from equilibrium
default: 1
gid Optional ID of GEOMETRY
default: not used
Description

This command is used to define mass damping and viscous damping for a given subset of the model. If a geometry ID (gid) is defined, then only those nodes/particles located inside the geometry will be damped. The mass damping force $\mathbf{F}_i$ acting on a node $i$ is defined as:

$\displaystyle{ \mathbf{F}_i = \left\{ \begin{array}{rcl} -C \cdot m_i \cdot \mathbf{v}_i & : & \mathrm{when \; moving \; towards \; equilibrium} \\ -sf \cdot C \cdot m_i \cdot \mathbf{v}_i & : & \mathrm{when \; moving \; away \; from \; equilibrium} \end{array} \right. }$

where $C$ is the damping coefficient defined by the CURVE or FUNCTION with ID cid, $m_i$ is the node mass and $\mathbf{v}_i$ is the node velocity. Whether the state is moving towards equilbrium or not is automatically determined by looking at the energy levels.

The viscous damping is defined as an artificial material viscosity (not active for entype=SPH). This viscosity produces an extra, strain rate dependent, stress term $\boldsymbol{\sigma}_\mu$:

$\displaystyle{ \boldsymbol{\sigma}_\mu = \frac{\mu}{c_{dec}} \int_0^t \dot{\boldsymbol{\varepsilon}}(\tau) \cdot \mathrm{e}^{(\tau-t)/c_{dec}} \mathrm{d}\tau }$
Example
Viscous damping

A complete model of two tip loaded cantilever beams, one with applied viscous damping and one without.

*UNIT_SYSTEM
SI
#
# --- PARAMETERS ---
#
*PARAMETER
mu = 1.0e7, "viscous damping coefficient 1"
cdec = 1.0e-5, "viscous damping coefficient 2"
F = 2000, "tip load"
#
# --- TIME ---
#
*TIME
0.01
#
# --- MESH ---
#
*COMPONENT_BOX
"undamped cantilever"
1, 1, 10, 1, 1
0, 0, 0, 0.1, 0.01, 0.01
*COMPONENT_BOX
"damped cantilever"
2, 2, 10, 1, 1
0, 0.05, 0, 0.1, 0.06, 0.01
*CHANGE_P-ORDER
ALL, 0, 2
#
# --- MATERIAL ---
#
*MAT_ELASTIC
1, 7800.0, 210.0e9, 0.3
#
# --- PART ---
#
*PART
"undamped cantilever"
1, 1
"damped cantilever"
2, 1
#
# --- BC ---
#
*BC_MOTION
1
G, 1, XYZ
*GEOMETRY_BOX
1
-0.001, 0, 0, 0.001, 0, 0
#
# --- TIP LOAD ---
#
*LOAD_FORCE
G, 2, Z, 1
*FUNCTION
1
-%F
*GEOMETRY_BOX
2
0.099, 0, 0, 0.101, 0, 0
#
# --- DAMPING ---
#
*LOAD_DAMPING
P, 2, 0, [%mu], [%cdec]
*END
Viscous damping applied to a cantilever beam
Viscous damping applied to a cantilever beam
Mass damping and the use of $sf \gt 1$ for faster dynamic relaxation

An elastic cantilever beam is exposed to a static pressure load. Mass damping helps us approach the static equilibrium. Note that FREQUENCY_CUTOFF is applied to increase the critical time step size.

*UNIT_SYSTEM
SI
#
# --- PARAMETERS ---
#
*PARAMETER
L = 0.2, "cantilever length"
h = 0.002, "cantilever width"
W = 0.02, "cantilever thickness"
q = 1.0e4, "pressure load"
C = 100.0, "mass damping coefficient 1"
sf = 10.0, "mass damping coefficient 2"
#
# --- TIME and OUTPUT ---
#
*TIME
0.1
*OUTPUT_SENSOR
"tip"
1, 1, [%L], [%W/2], [%h/2]
*FREQUENCY_CUTOFF
1
ALL, 0, 2.0e-6
#
# --- MESH ---
#
*COMPONENT_BOX
"cantilever"
1, 1, 20, 2, 1
0, 0, 0, [%L], [%W], [%h]
*CHANGE_P-ORDER
ALL, 0, 3
#
# --- MATERIAL ---
#
*MAT_ELASTIC
1, 7800.0, 210.0e9, 0.3
#
# --- PART ---
#
*PART
"cantilever"
1, 1
#
# --- BC ---
#
*BC_MOTION
1
G, 1, XYZ
*GEOMETRY_BOX
1
-0.001, 0, 0, 0.001, 0, 0
#
# --- PRESSURE LOAD ---
#
*LOAD_PRESSURE
G, 2, 102
*GEOMETRY_SEED_COORDINATE
2
[%L/2], [%W/2], [%h]
*FUNCTION
102
%q
#
# --- DAMPING ---
#
*LOAD_DAMPING
P, 1, 101, 0, 0, [%sf]
*FUNCTION
101
[%C]
*END
Cantilever beam exposed to a distributed load
Cantilever beam exposed to a distributed load