can be used to detect the time in a quasi-static uni-directional
Abaqus/Explicit
simulation when a steady-state condition has been reached and then terminate
the simulation;
can be used to output quantities that are useful in tracking the
progress of a uni-directional
Abaqus/Explicit
simulation; and
Many types of uni-directional processes are used to transform preformed
shapes into forms more suitable for further processing. The most common
examples are rolling, wire drawing, and extrusion processes. Since the
processes are usually carried out at low speeds, explicit dynamic procedures
such as those in
Abaqus/Explicit
are often used to model the processes as quasi-static. The analyses usually
consist of a workpiece that is formed into a desired shape by any number of
rollers or other forming surfaces along a primary direction. The forming
surfaces are usually modeled as rigid bodies. For rolling simulations the rigid
body reference node is usually defined at the center of the roller. The mesh of
the workpiece is often extruded and may be constructed of multiple layers of
material. As the workpiece progresses through the forming surfaces, the shape
eventually reaches a constant state. The position where the workpiece exits the
final forming surface is referred to as the exit plane and is usually aligned
with the rigid body reference node of the final forming surface. As soon as
this constant shape is reached, the analysis is considered to have reached
steady state. The force and torque on the final forming surfaces at this
steady-state condition have also reached constant values or oscillate about
constant values. A significant computational savings can be achieved by
detecting the steady-state condition and halting the analysis either
immediately or as soon as the steady-state cross-section progresses beyond the
exit plane to a position referred to as the cutting plane.
Mesh Requirements
The workpiece mesh is required to meet certain conditions for use with the
steady-state detection capability. First, the mesh must be topologically
regular in the primary direction. In other words, the mesh should consist of
multiple planes of elements with each plane being similar to its adjacent
leading and trailing planes in that it contains the same number of elements and
the same element topology in the cross-section. Furthermore, each element in a
plane is connected to elements in leading and trailing planes that reference
the same material and section properties. Therefore, meshes with multiple
materials and section properties are permitted, but any row of elements in the
primary direction must be of the same type and must reference the same material
and section properties (see
Figure 1).
Figure 1. Acceptable multiple-material extruded mesh for a rolling
analysis.
Steady-State Detection Criteria Sampling
To determine if steady state has been reached, steady-state detection
“norms” are calculated, which represent an averaged value of a variable of
interest over the cross-section of the workpiece as material passes through a
given position along the primary direction. This position is referred to as the
exit plane and usually coincides with the position of the last rigid forming
tool (e.g., roller) that the workpiece passes through. The normal of the exit
plane is by definition coincident with the primary direction. The time
intervals at which the norms are sampled vary depending on whether the rolling
analysis is modeled in an Eulerian or Lagrangian manner.
Sampling in a Lagrangian Analysis
In a Lagrangian-based analysis (which may include adaptive meshing employed
on a Lagrangian domain) the steady-state norms are calculated as the trailing
control node of each plane of elements passes the exit plane.
Figure 2
illustrates the control node definitions.
Figure 2. Control node positioning.
The time period of norm sampling is, therefore, based on the frequency at
which the planes of elements cross the exit plane. For output purposes the
values of the norms are assumed to remain constant between the times at which
successive control nodes pass the exit plane.
Sampling in an Eulerian Analysis
An Eulerian analysis employs a control volume approach in which material is
drawn from an inflow Eulerian boundary and is pushed or pulled out through an
outflow boundary. Adaptive mesh domains are defined on the workpiece, and
sliding boundary regions are defined to model contact between the workpiece and
forming tools such as rollers. See
About ALE Adaptive Meshing
for details of adaptive meshing techniques. The mesh remains relatively
stationary while the material moves through the exit plane. The time period
between sampling is, therefore, based on the progress of the material moving
through the exit plane. To determine a time period in a manner consistent with
the Lagrangian case, the sampling period is determined by dividing the
characteristic element length of the workpiece by the speed of the material
flow. This period is roughly the time it takes for material to pass through an
element of typical size.
Steady-State Detection Norm Definitions
An individual norm is considered to have achieved steady state if its
relative change in value over three consecutive planes does not exceed a
tolerance. You can provide the norm tolerances when you define the steady-state
criteria, or default values of tolerances can be chosen by
Abaqus/Explicit.
The norms can be output by requesting their identifiers listed in the
definitions below.
Equivalent Plastic Strain Norm
The plastic strain norm of a plane of elements is defined by summing the
product of the equivalent plastic strain and the element volume of each element
on the plane, then dividing by the total volume of the elements on the plane.
This norm provides a weighted average of the equivalent plastic strain for the
plane. The identifier for the equivalent plastic strain norm is
SSPEEQ.
Spread Norm
The spread norm of a plane of elements is computed as the largest of the
area moments of inertia of the cross-section of the plane. In determining the
spread norm, the cross-section of the plane of elements is determined by
projecting the element faces whose normals originally coincided with the
primary direction onto the exit plane. The area moments of inertia are then
determined about the centroid of the section in the directions of the original
principal axes of the cross-section. The identifier for the spread norm is
SSSPRD.
Force Norm
The force norm is computed by averaging the magnitude of the force at the
rigid body reference node of a forming tool, such as the exit roller, over the
time period between sampling points. You provide the rigid body reference node
and force direction. The identifier for the force norm is
SSFORC.
Torque Norm
The torque norm is computed by averaging the magnitude of the torque at the
rigid body reference node of a forming tool, such as the exit roller, over the
time period between sampling points. You provide the rigid body reference node
and torque direction. The identifier for the torque norm is
SSTORQ.
Requesting Steady-State Detection during an Analysis
You must define the criteria that are used to determine if steady state has
been reached.
Abaqus/Explicit
will halt the analysis based on the achievement of steady state.
Steady-State Detection
A steady-state detection definition is used to define the elements in the
workpiece, the primary direction of the workpiece, the cutting position, and
the type of sampling used. The primary direction is defined by specifying the
direction cosines with respect to the global Cartesian coordinate system. The
cutting position is defined by specifying the global coordinates of a point
lying in the cutting plane. The normal to the cutting plane is assumed to
coincide with the primary direction. Once steady state has been detected, the
analysis is terminated when the plane of the workpiece that was first detected
to have reached steady state has progressed to the cutting plane. You can
choose the sampling method used, as described below.
Requesting Sampling as Elements Pass the Exit Plane for a Lagrangian Analysis
You can request that all steady-state norms be calculated as each plane of
elements crosses the exit plane.
Requesting Sampling at Uniform Intervals for an Eulerian Analysis
Alternatively, you can request that all steady-state norms be calculated
at an interval based on the time required for material to progress the length
of an average element.
Any number of steady-state criteria definitions can be specified. Only when
all of the criteria specified under any one steady-state criteria definition
have been satisfied will the analysis be considered to have reached steady
state.
To define the criteria, you specify the norm type identifier, the norm
tolerance, and the global coordinates of a point on the exit plane. For force
and torque norms, you also specify the rigid body reference node of the forming
tool at the exit plane and the direction cosines of the force or torque. Exit
planes can be defined separately for each norm definition.
Input File Usage
Use the following options to define the criteria needed to
achieve steady state:
For example, assume that two sets of criteria are of interest
and that the analysis can be terminated as soon as either is satisfied. The
input might be as follows:
Steady-state detection is intended to be used with plasticity-based
materials since the equivalent plastic strain norm would be zero for
nonplasticity-based material models.
Procedures
One steady-state detection definition is allowed per analysis. The
definition can be entered in any step and is continued through subsequent steps
in an analysis. A steady-state detection definition cannot be entered in an
annealing step or continued through an annealing step.
Elements
The current steady-state detection capabilities support the use of C3D8R and C3D8RT elements only.
Output
The output variables
SSPEEQn,
SSSPRDn,
SSFORCn, and
SSTORQn are used to
output the equivalent plastic strain, spread, force, and torque norms,
respectively.
Abaqus/CAE
can be used to obtain history plots of each of the steady-state detection norm
variables. Individual norms can be output by requesting the norm number
n, which is based on the order in which the norms
are specified. Referring to the example above, if the force norm of the second
steady-state criteria definition were to be requested, the output identifier
would be SSFORC3. If a steady-state detection norm
is requested that does not include a norm number,
SSFORC for example, all norms of that type are
output.
Once steady state has been detected, an element set is created automatically
by
Abaqus/Explicit
and written to the output database consisting of the plane of elements that
first satisfied the steady-state criteria. The element set created is named
SteadyStatePlane-StepN, where
N is the step number; and it
can be viewed with
Abaqus/CAE.
If no output requests are made to the output database, the element set
SteadyStatePlane-StepN is not created.
Input File Template
HEADING
…
ELSET, ELSET=WORKPIECE
*************************
STEPDYNAMIC, EXPLICITData line to specify the time period of the step
...
STEADY STATE DETECTION, ELSET=WORKPIECE, SAMPLING=PLANE BY PLANEData line specifying rolling direction and cutting plane positionSTEADY STATE CRITERIAData lines specifying steady-state detection norm criteria
...
OUTPUT, HISTORY, TIME INTERVAL=1.E-6INCREMENTATION OUTPUTSSPEEQ, SSSPRD, SSFORC, SSTORQ
...
END STEP
