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Abaqus/CAE Usage: Step module: Create Step: General, Dynamic, Explicit or Dynamic, Temp-disp, Explicit: Mass scaling: Use scaling definitions below: Create: Semi-automatic mass scaling, Scale: At beginning of step or Throughout step, Region: Set: elset
Example 1
Different mass scaling factors may be useful when materials with vastly different wave speeds or mesh refinements are present in an analysis. In this example a scale factor of 50 may be desirable for the masses of all elements in a quasi-static analysis, except for a few elements for which a mass scaling factor of 500 is used.
*FIXED MASS SCALING, FACTOR=50.0
*FIXED MASS SCALING, FACTOR=500.0, ELSET=elset1
The first fixed mass scaling definition scales the masses of all elements in the model by a factor of 50. The second fixed mass scaling definition overrides the first definition for the elements contained in element set elset1 by scaling their masses by a factor of 500.
Example 2
An alternative method of scaling the masses of elements in elset1 is to assign a stable time increment to them and allow Abaqus/Explicit to determine the mass scaling factors.
*FIXED MASS SCALING, FACTOR=50.0
*FIXED MASS SCALING, DT=.5E-6, TYPE=BELOW MIN, ELSET=elset1
The first fixed mass scaling definition scales the masses in the entire model by a factor of 50. The second fixed mass scaling definition overrides the first definition by scaling the masses of any elements in elset1 whose stable time increments are less than .5 × 10−6 .
Mass scaling at the beginning of the step
Fixed mass scaling is used to prescribe mass scaling only at the beginning of a step and always scales the original element masses. When the scale factor is defined directly, the mass is scaled by the value assigned to the scale factor. If the element-by-element stable time increment, dt, is specified, the mass scaling is based on this value. If both the scale factor and the element-by-element stable time increment are specified, the mass is first scaled by the value assigned to the scale factor and then possibly scaled again, depending on the value assigned to the element-by-element stable time increment and the type of fixed mass scaling chosen.
Local mass scaling can be defined for a specific element set. If no element set is specified, the fixed mass scaling definition will apply to all elements in the model. Only one fixed mass scaling definition is permitted per element set. Multiple fixed mass scaling definitions cannot contain overlapping element sets. Local mass scaling definitions will overwrite global definitions for the specified element sets.
Input File Usage: *FIXED MASS SCALING, FACTOR=factor, DT=dt, \mathrm { T Y P E = } t y p e , \mathrm { E L S E T = } e l s e t
Abaqus/CAE Usage: Step module: Create Step: General, Dynamic, Explicit or Dynamic, Temp-disp, Explicit: Mass scaling: Use scaling definitions below: Create: Semi-automatic mass scaling, Scale: At beginning of step, Scale by factor: factor, Scale to target time increment of: dt
Example
Assume that for a quasi-static analysis a mass scaling factor of 50 is applied to all the elements in the model. Furthermore, assume that even after being scaled by a factor of 50, a few extremely small or poorly shaped elements are causing the stable time increment to be less than a desired minimum. To increase the stable time increment, the following option is used:
\star \mathrm F T X E D ~ \mathbb { M a S S } ~ \index { S C a L I N G } , \quad \mathtt { F A C T O R = 5 0 } ~ . , \quad \mathtt { T Y P E = B E L O W } ~ \mathbb { M T N } , \quad \mathbb { D } \mathbb { T } = \dots \mathbb { S } \mathbb { E } - 6 \mathbb { N } ,
The specified scale factor causes the masses of all the elements in the model to be scaled by a factor of 50. If any element’s stable time increment is still below 0 . 5 \times 1 0 ^ { - 6 } after being scaled by a factor of 50.0, its mass will be scaled such that its stable time increment is equal to 0 . 5 \times 1 0 ^ { - 6 } .
Mass scaling throughout the step
Variable mass scaling with a specified element-by-element stable time increment is used to define mass scaling that is to be performed at the beginning and throughout the step. Either the frequency in increments or the number of intervals must be specified to define how frequently mass scaling is to be performed. In increments other than those in which mass scaling is performed, the time increment used will generally be different from the value assigned to the element-by-element stable time increment.
Local mass scaling can be defined for a specific element set. If no element set is specified, the variable mass scaling definition will apply to all elements in the model. Only one variable mass scaling definition is permitted per element set. Multiple variable mass scaling definitions cannot contain overlapping element sets. Local mass scaling definitions will overwrite global definitions for the specified element sets.
Input File Usage: * \mathrm { V A R I A B L E ~ M A S S ~ S C A L I N G } , \mathrm { D T } = d t , \mathrm { T Y P E } = t y p e , \mathrm { E L S E T } = e l s e t
Abaqus/CAE Usage: Step module: Create Step: General, Dynamic, Explicit or Dynamic, Temp-disp, Explicit: Mass scaling: Use scaling definitions below: Create: Semi-automatic mass scaling, Scale: Throughout step, Scale to target time increment of: dt
Calculating the mass scaling at equally spaced increments
You can specify the number of increments between mass scaling calculations. For example, specifying a frequency of 5 will cause mass scaling to be performed at the beginning of the step and at increments 5, 10, 15, etc.
Care should be taken when choosing the value of the frequency, since performing mass scaling every few increments during an analysis may result in noticeable additional computational cost per increment.
Input File Usage: * \mathrm { V A R I A B L E ~ M A S S ~ S C A L I N G } , \mathrm { T Y P E } = t y p e , \mathrm { D T } = d t , \mathrm { F R E Q U E N C Y } = n
Abaqus/CAE Usage: Step module: Create Step: General, Dynamic, Explicit or Dynamic, Temp-disp, Explicit: Mass scaling: Use scaling definitions below: Create: Semi-automatic mass scaling, Scale: Throughout step, Scale to target time increment of: dt, Scale: Every n increments
Calculating the mass scaling at equally spaced time intervals
Alternatively, you can specify the number of equally spaced time intervals at which the mass scaling calculations are to be performed. For example, specifying 5 intervals in a step with a duration of one second will cause mass scaling to be performed at the beginning of the step and at times of .2 , .4, .6, .8, and 1.0 seconds.
Input File Usage: *VARIABLE MASS SCALING, TYPE=type, DT=dt, NUMBER INTERVAL=n
Abaqus/CAE Usage: Step module: Create Step: General, Dynamic, Explicit or Dynamic, Temp-disp, Explicit: Mass scaling: Use scaling definitions below: Create: Semi-automatic mass scaling, Scale: Throughout step, Scale to target time increment of: dt, Scale: At n equal intervals
Different mass scaling at the beginning and during the step
There are cases where it is desirable to include mass scaling at the beginning of a step that may be modified further throughout the step.
Input File Usage: Use both of the following options: *FIXED MASS SCALING, FACTOR=factor, TYPE=type, DT=dt_init *VARIABLE MASS SCALING, TYPE=type, DT=dt_min, FREQUENCY=n or NUMBER INTERVAL=n
Abaqus/CAE Usage: Create both of the following mass scaling definitions: Step module: Create Step: General, Dynamic, Explicit or Dynamic, Temp-disp, Explicit: Mass scaling: Use scaling definitions below: Create: Semi-automatic mass scaling, Scale: At beginning of step Semi-automatic mass scaling, Scale: Throughout step
Example
Assume that in a dynamic impact analysis, a few extremely small or poorly shaped elements exist in the mesh and consequently control the stable time increment. To prevent these elements from controlling the stable time increment, it is desirable to scale their masses at the beginning of the step. In addition, elements in a region of the mesh will develop severe distortions as a result of impact with a fixed rigid surface. Consequently, elements in the impact zone may eventually control the stable time increment.
Since the elements in the impact zone are essentially stationary against the rigid surface, selectively scaling their masses will guarantee that the overall dynamic response is not adversely affected. Mass scaling these elements by prescribing a time increment to limit the reduction in the element-by-element stable time increment may decrease run time substantially.
For example, specify fixed mass scaling for all elements in the model with stable time increments below a value of 1 . 0 \times 1 0 ^ { - 6 } . In addition, specify variable mass scaling for the elements in the impact zone (elset1) with stable time increments below a value of 0 . 5 \times 1 0 ^ { - 6 } . In this case all the elements in the model are checked at the beginning of the step. If any have stable time increments less than 1 . 0 \times 1 0 ^ { - 6 } , their masses are scaled (independently) such that the element-by-element stable time increment equals 1 . 0 \times 1 0 ^ { - 6 } . This scaling remains in effect throughout the step and is not further modified, except for those elements in elset1. The variable mass scaling definition causes the elements contained in elset1 to be scaled throughout the step so that their stable time increments do not become less than 0 . 5 \times 1 0 ^ { - 6 } . Because only elements in elset1 are scaled during the step, it is possible that a stable time increment less than 0 . 5 \times 1 0 ^ { - 6 } may result.
Mass scaling in a multiple step analysis
The scaled element masses at the end of one step and any variable mass scaling methods specified in that step are carried forward automatically to the subsequent step, ensuring continuity in the mass matrix at the step boundaries and continued application of the variable mass scaling methods. However, you can reset the element masses to their original values or recompute the element masses by using a new fixed mass scaling method at the beginning of the subsequent step. You can also remove the variable mass scaling methods inherited from the prior step or replace an inherited method with a new variable mass scaling method.
To reset the initial mass matrix, specify a fixed mass scaling method in the subsequent step. Similarly, specify a variable mass scaling method in the subsequent step to discontinue all of the variable mass scaling methods of the prior step. The examples below illustrate the following special cases: (a) continuous mass matrix with no further mass scaling, and (b) reverting the mass matrix to the original state with no further mass scaling.
Very large changes in element mass across the steps due to mass scaling may lead to precision problems in the mass calculations. These precision problems may give rise to erroneous or misleading results. When large changes in element masses are desired in such situations, it is recommended that fixed mass scaling be used in the new step to reset the element masses to their original values before using additional mass scaling definitions, as required, to scale the element masses to their desired values.
Continuous mass matrix with no further scaling
To define a continuous mass matrix with no further scaling, remove any variable mass scaling definitions inherited from the prior step by redefining a new variable mass scaling definition.
Input File Usage: Use the following option without any parameters in a new step: \mathrm { \mathrm { * V A R I A B L E ~ M A S S ~ S C A L I N G } }
Abaqus/CAE Usage: Step module: Create Step: General, Dynamic, Explicit or Dynamic, Temp-disp, Explicit: Mass scaling: Use scaling definitions below: Create: Disable mass scaling throughout step
Example
Assume that during the first step of a quasi-static analysis, elements will experience distortions that will cause the stable time increment to decrease dramatically. Furthermore, assume that the deformation during the second step will not be large enough to have any further effect on the stable time increment.
*HEADING
...
*STEP
...
*FIXED MASS SCALING, FACTOR=1.1
*VARIABLE MASS SCALING, TYPE=BELOW MIN, DT=1.E-5, FREQUENCY=10
...
*END STEP
*STEP
...
*VARIABLE MASS SCALING
...
*END STEP
During the first step the fixed mass scaling increases the element mass by the factor 1.1. The variable mass scaling definition scales the mass of the entire model at the beginning of the step and every tenth increment such that the element-by-element stable time increment equals at least 1 × 10−5 . The variable mass scaling definition in the second step replaces the one continued from the first step. This particular definition of variable mass scaling without any parameters in the second step also prevents any further mass scaling during the second step. The scaled mass matrix from the first step is carried over to be used during the entire second step.
Reverting the mass matrix to the original state
You can introduce a fixed mass scaling method in the subsequent step to discontinue all of the mass scaling methods of the prior step. Further, if the default specification of fixed mass scaling is used, element masses revert to their original values at the beginning of the subsequent step. Thus, specify just the default fixed mass scaling method to prevent the scaled mass of the previous step from being used in a new step. This is useful going from a quasi-static simulation step where mass scaling is appropriate to a dynamic step in which no scaling is desired.
Input File Usage: Use both of the following options without any parameters:
*FIXED MASS SCALING
*VARIABLE MASS SCALING
Abaqus/CAE Usage: Create both of the following mass scaling definitions:
Step module: Create Step: General, Dynamic, Explicit or
Dynamic, Temp-disp, Explicit: Mass scaling: Use scaling
definitions below: Create:
Reinitialize mass
Disable mass scaling throughout step
Example
Assume that an analysis contains a quasi-static step followed by a dynamic step. Mass scaling can be performed during the quasi-static step but turned off during the dynamic step.
*HEADING
*STEP
...
*FIXED MASS SCALING, FACTOR=1.1
*VARIABLE MASS SCALING, TYPE=BELOW MIN, DT=1.E-5, FREQUENCY=10
*END STEP
*STEP
*FIXED MASS SCALING
*VARIABLE MASS SCALING
*END STEP
During the first step the fixed mass scaling increases the element mass by the factor 1.1. The variable mass scaling definition scales the mass of the entire model at the beginning of the step and every tenth increment such that the element-by-element stable time increment equals at least 1 × 10−5 . The new fixed mass scaling definition without any parameters in the second step then reverts the mass matrix back to the original state. The new variable mass scaling definition replaces all the variable mass scaling definitions inherited from the first step. Further, since the new variable mass scaling definition has no parameters, no mass scaling is applied during the second step. Thus, the mass matrix for the second step reverts to that of the original state.
Mass contribution from external programs connected to Abaqus via co-simulation
Co-simulation can lead to mass and/or rotary inertia from external programs being added to the Abaqus model during a step. However, that contribution along with other quantities imported from the external program must be removed once the co-simulation step is completed. If co-simulation is expected to add mass and/or rotary inertia to the Abaqus model, Abaqus automatically reverts the mass matrix back to the original state once such a co-simulation step is completed. You need to respecify any mass scaling that must be continued beyond the co-simulation step.
When mass scaling is or is not used
The following entities are not affected by mass scaling:
• Thermal solution response in a fully coupled thermal-stress analysis
• Gravity loads, viscous pressure loads
• Adiabatic heat calculations
• Equation of state materials
• Fluid and fluid link elements
• Surface-based fluid cavities
• Spring and dashpot elements
Densities associated with any of the relevant items in this list will remain unscaled. Mass, rotary inertia, infinite, and rigid elements can be scaled. However, because none of the elements has an associated stable time increment, they can be scaled only using either a user-specified scale factor or an element-
by-element stable time increment applied uniformly. If the element-by-element stable time increment is specified, at least one element with a stable time increment must be included in the mass scaling definition. Rotary inertia in shell, beam, and pipe elements is based on the scaled mass.
The mass of infinite elements can be scaled; however, the infinite elements will not act as quiet boundaries unless the densities of each adjacent deformable element are scaled by the same factor. The mass of both elements will be scaled by the same factor if they are both included in the same fixed or variable mass scaling definition.
Automatic mass scaling for analysis of bulk metal rolling
Bulk metal rolling is generally considered a quasi-static process, but the process is often modeled with Abaqus/Explicit because of its ability to handle the contact problem well. To achieve an economical solution with Abaqus/Explicit, it is often useful to increase the mass of the product artificially. However, the mass scaling factor must be chosen such that the changes in the mass and the corresponding changes in the inertial forces do not alter the solutions significantly. Choosing too high a scaling factor will not produce quasi-static results. Choosing too low a scaling factor, while conservative, will result in long run times. Rolling variable mass scaling can be used to make the choice of the optimal scaling factor automatic for this process.
The automatic strategy is based on the semi-automatic method of scaling all elements to have equal element stable time increments. The method is made automatic by determining the appropriate value for the target stable time increment from several parameters of the rolling process. The value used for the target stable time increment, \Delta t , is based on the average element length in the rolling direction, L _ { e } ; ; the feed rate, V ; and the number of nodes in the cross-section of the product, n. The feed rate is defined as the average velocity of the product in the rolling direction during steady-state conditions. The value of \Delta t is adjusted during the analysis to account for the actual value of the feed rate. You must specify estimated values for the average velocity, the average element length in the rolling direction, and the number of nodes in the cross-section of the product.
The mass of any element will never drop below its original mass. This is different from the method of scaling all elements to have equal element stable time increments. Imposing this restriction means that rolling problems that have significant inertial effects will not have their mass adjusted automatically when they are analyzed as quasi-static.
To achieve a good result, it is recommended that:
• the product be meshed by extruding a two-dimensional cross-section of the product;
• the average element length in the rolling direction not vary significantly along the length of the product;
• the product have an initial velocity in the rolling direction approximately equal to the steady-state feed rate;
• the element size in the cross-section be equal to or less than the size in the rolling direction; and
• no other mass scaling be used on elements scaled with rolling automatic variable mass scaling.
Input File Usage:
*VARIABLE MASS SCALING, ELSET=elset1, FREQUENCY=n, TYPE=ROLLING, FEED RATE=V, EXTRUDED LENGTH= , CROSS SECTION NODES=n
Abaqus/CAE Usage: Step module: Create Step: General, Dynamic, Explicit or Dynamic, Temp-disp, Explicit: Mass scaling: Use scaling definitions below: Create: Automatic mass scaling, Feed rate: V, Extruded element length: L _ { e } , Nodes in cross section: n
Output
Output variable EMSF provides the element mass scaling factor. Abaqus/CAE can be used to obtain contour and history plots of EMSF. Output variable DMASS provides the total percent change in mass of the model as a result of mass scaling and is available for history plotting in Abaqus/CAE. Output variable DMASS is not available on an element set basis.
Output variable EDT provides the element stable time increment. The element stable time increment includes the effect of mass scaling. Abaqus/CAE can be used to obtain history plots of EDT.
11.7 Selective subcycling
• “Selective subcycling,” Section 11.7.1