7.2.4 Time integration accuracy in transient problems

Products: Abaqus/Standard Abaqus/CAE

References

Overview

Abaqus/Standard usually uses automatic time stepping schemes for the solution of transient problems. Abaqus/Standard provides tolerance parameters to indicate the level of accuracy required in the approximate time integration of transient effects that have a physical time scale. You can modify the parameters that control the increase and reduction of the time increment size.

Time incrementation parameters and adjustment criteria

The following tolerance parameters are available for specific analysis procedures:

Procedure	Accuracy measure	Tolerance
Implicit dynamics (“Implicit dynamic analysis using direct integration,” Section 6.3.2)	Half-increment residual	Half-increment residual tolerance
Transient heat transfer analysis (“Uncoupled heat transfer analysis,” Section 6.5.2)	Temperature increment,
Consolidation analysis (“Coupled pore fluid diffusion and stress analysis,” Section 6.8.1)	Pore pressure increment,
Creep and viscoelastic material behavior (“Rate-dependent plasticity: creep and swelling,” Section 22.2.4)		Creep tolerance

In any transient analysis where automatic time incrementation is used, some of these tolerances,

, will be active. Corresponding measures of the integration accuracy,

, will be calculated for each increment in the step. Abaqus/Standard will use these values to adjust the time incrementation using the criteria described in this section. The smallest time increment required by all criteria is used if more than one accuracy measure is active.

Reducing the time increment size

If for any control, J, that is active in the step, the time increment is too large to satisfy that time integration accuracy requirement. The increment is, therefore, begun again with a time increment of

where you can define the value of

. By default,

= 0.85.

Input File Usage:

*CONTROLS, PARAMETERS=TIME INCREMENTATION
first data line
 , , ,

Abaqus/CAE Usage:

Step module: OtherGeneral Solution ControlsEdit: toggle on Specify: Time Incrementation; click More to see additional data tables

Increasing the time increment size

If at the current time increment, ,

for all J in each of

consecutive increments, i, and if no cut-back has occurred within those increments because of nonlinearity, the next time increment will be increased to

You can define the values of

, and

. By default,

= 3,

= 0.75, and

= 0.8.

is the proposed new time increment, which is defined as

for transient heat transfer and transient mass diffusion problems and which is defined as

for other transient problems.

A limit, , is placed on the time increment increase factor. The default value of depends on the type of analysis:

= 1.25 for dynamic analysis
= 2.0 for diffusion-dominated processes: creep, transient heat transfer, coupled temperature-displacement, soils consolidation, and transient mass diffusion
= 1.5 for all other cases

You can redefine

for each analysis type.

If the problem is nonlinear, the time increment may be restricted by the rate of convergence of the nonlinear equations. The time incrementation controls used with nonlinear problems are described in “Convergence criteria for nonlinear problems,” Section 7.2.3.

Input File Usage:

*CONTROLS, PARAMETERS=TIME INCREMENTATION
 , , , , , , , , , 
 , , , , , , , 
, , ,

Abaqus/CAE Usage:

Step module: OtherGeneral Solution ControlsEdit: toggle on Specify: Time Incrementation; click More to see additional data tables

Time increment changes during implicit integration procedures

In linear transient problems when Abaqus/Standard uses implicit integration, the Jacobian must be reformed whenever the time increment changes. Therefore, to reduce the number of increments at which such decomposition of the system matrix must occur, Abaqus/Standard makes use of the factor , where

The definition of

results in the following inequality between the proposed and the current time increments:

Based on this inequality the time increment is allowed to increase only when its value computed by the criteria described earlier in this section, or computed using the value of PNEWDT specified in certain user subroutines (UMAT, for example), is greater than or equal to

. The default value of

is 1.0, but you can redefine it to be a smaller number. Reducing

to a value less than 1.0 allows the time increment to increase by a factor that is smaller than

, thereby forcing a time increment change, even if the change is small. Otherwise, the solution continues with the same

Input File Usage:

*CONTROLS, PARAMETERS=TIME INCREMENTATION
first data line
second data line
 , , , ,

Abaqus/CAE Usage:

Step module: OtherGeneral Solution ControlsEdit: toggle on Specify: Time Incrementation; click More to see additional data tables