7.2.4 Time integration accuracy in transient problems

**Products: **ABAQUS/Standard ABAQUS/CAE

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-step residual | Half-step 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 6.7.1) | Pore pressure increment, | |

Creep and viscoelastic material behavior (“Rate-dependent plasticity: creep and swelling,” Section 18.2.4) | Creep tolerance |

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 |

ABAQUS/CAE Usage: | Step module: Specify: Time Incrementation; click More to see additional data tables |

If at the current time increment, ,

for all

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

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: 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

Input File Usage: | *CONTROLS, PARAMETERS=TIME INCREMENTATION |

ABAQUS/CAE Usage: | Step module: Specify: Time Incrementation; click More to see additional data tables |