Path-following (or continuation) procedures are used to describe the unstable responses of structures exhibiting snap-back or snap-through phenomena. These methods consist in adapting the external load during the deformation process in order to satisfy a control constraint, by introducing an additional unknown, the load multiplier. Several variants exist depending on the controlled quantity: degrees of freedom, strain measures, or variables related to energy dissipation.
In addition to enabling the tracing of unstable responses, a major advantage of these approaches lies in improving the convergence of incremental Newton-type solvers by reducing the number of iterations required. This gain often compensates for the additional computational cost associated with the continuation algorithm. Some formulations have proven both efficient and simple to implement.
However, no objective criterion yet allows one to determine which formulation is best suited for the simulation of reinforced concrete structures, where multiple dissipation mechanisms coexist along with a strong spatial variability of the material properties.
The proposed postdoctoral work aims to develop robust path-following algorithms for such structures, building upon previous research carried out at CEA. It will include a critical analysis of existing formulations, an evaluation of their performance (monolithic or partitioned solvers), followed by their implementation. Finally, representative test cases of industrial structures will be simulated to assess the gain in robustness and computational cost compared to standard solvers.