u2.04.07 Use of transient resolution methods for highly nonlinear, almost static problems

Summary:

This document presents the use of transient resolution methods (implicit or explicit) for the numerical simulation of quasistatic problems with strong material nonlinearities. We only seek to obtain solutions where the dynamic effects are negligible.

These resolution methods (based on the use of DYNA_NON_LINE) are designed as an alternative to the usual quasistatic approaches of Code_Aster (based on STAT_NON_LINE) when they are unable to converge in an acceptable amount of time. This may be the case for applications involving damaging materials.

The methods that are the subject of this document are of two types:

1. implicit transitory resolution,

2. explicit pseudo-dynamic resolution.

The choice will depend on the nature of the problem to be treated, in particular, in relation to the time scale considered. Since the use of these strategies is more delicate than the semi-static approach, they should be reserved for the most problematic cases.

Reading the U2.06.13 documentation is a highly recommended prerequisite: the general advice for using DYNA_NON_LINE remains relevant.

u2.04.07 Table of contents

• 1. Introduction
• 2. Features available in semi-static mode and absent in transient
• 3. Transition from a quasistatic calculation to a transitory calculation
• 4. Digital implementation
  • 4.1. Discretization in time
  • 4.2. Choice of integration schemes in time
  • 4.3. Depreciation models
  • 4.4. Adaptation of explicit methods
• 5. Quality control of calculated solutions
  • 5.1. Quantities of interest from the quasistatic
  • 5.2. Additional dynamic quantities to be analyzed
  • 5.3. Analysis examples
• 6. Optimizing performance
• 7. Conclusion
• 8. Bibliography