r5.03.81 Method IMPLEX

Summary:

This document presents a method for solving the non-linear problem, due to Oliver et al. [1], substituting Newton’s method for some laws of damage behavior and plasticity (ENDO_FRAGILE [3], ENDO_ISOT_BETON [4], and VMIS_ISOT_LINE [] and [5] at present). It is based on an explicit extrapolation of internal variables to determine the degrees of freedom (displacement) from which behavior is implicitly integrated. The nullity of the residue is not verified. It therefore introduces an approximation of the resolution but makes it possible to guarantee the robustness of the calculation.

It is therefore up to the user to take a critical look at the results obtained, as they are not converged in the classical sense of the term, and may potentially be far from the exact solution; it is therefore advisable to carry out several calculations with different load increments to ensure that the difference in results obtained is small.

In cases of sudden expansion of the damaged zone resulting in a strong snap-back of the overall force/displacement response, the method, while it makes it possible to overcome the instability, cannot be reliable in terms of result.

• 1. Introduction
• 2. Problem position
• 3. The IMPLEX method
  • 3.1. A 2-step method
  • 3.2. Automatic time step management
  • 3.3. Key points of the method
• 4. Practical aspects of use
• 5. Bibliography
• 6. Description of document versions