About Quasi-Static Steps

Incrementation

You can control the time incrementation in a quasi-static analysis directly, or it can be controlled automatically by Abaqus/Standard. Automatic incrementation is preferred in almost all cases.

If you specify the time increments in a quasi-static analysis directly, fixed time increments equal to the specified initial time increment will be used throughout the analysis, except when the explicit creep integration scheme is used. In this case Abaqus/Standard might decrease the time increment if the stability limit is exceeded.

If you select automatic incrementation, the size of the time increment is limited by the accuracy of the integration. The user-specified accuracy tolerance parameter limits the maximum inelastic strain rate change allowed over an increment.

Explicit Creep Integration

Nonlinear creep problems (Rate-dependent plasticity: creep and swelling) that exhibit no other nonlinearities can be solved efficiently by forward-difference integration of the inelastic strains if the inelastic strain increments are smaller than the elastic strains. This explicit method is efficient computationally because, unlike implicit methods, iteration is not required. Although this method is only conditionally stable, the numerical stability limit of the explicit operator is in many cases sufficiently large to allow the solution to be developed in a reasonable number of time increments.

For creep at very low stress levels, however, the unconditional stability of the backward difference operator (implicit method) is desirable. In such cases Abaqus/Standard will invoke the implicit integration scheme automatically.

Explicit integration can be less expensive computationally and simplifies implementation of user-defined creep laws in user subroutine CREEP; you can restrict Abaqus/Standard to using this method for creep problems (with or without geometric nonlinearity included). See Rate-dependent plasticity: creep and swelling for further details.

Integration Scheme for Viscoelasticity and Rate-dependent Yield

Problems including Time domain viscoelasticity are always integrated with an unconditionally stable operator. The time step in these problems is limited only by the accuracy tolerance parameter defined above.

Problems including Rate-dependent yield and Parallel rheological framework are always integrated using an implicit, unconditionally stable method. The accuracy tolerance parameter does not limit the inelastic strain rate change and can be set equal to any nonzero value to activate automatic time incrementation.

Local Instabilities

Some types of analyses might develop local instabilities, such as surface wrinkling, material instability, or local buckling. In such cases, it might not be possible to obtain a quasi-static solution, even with the aid of automatic incrementation. Abaqus/Standard offers the ability to stabilize this class of problems by applying damping throughout the model in such a way that the viscous forces introduced are sufficiently large to prevent instantaneous buckling or collapse but small enough not to affect the behavior significantly while the problem is stable. The available automatic stabilization schemes are described in detail in Automatic stabilization of unstable problems.