Interest of a segregated finite element solver for mechanical multi-physics coupling in geo-materials

Many civil engineering problems lead to coupled multi-physics formulations: among them are the classical poro-mechanical and non-local problems, and more recently the multiple chemical-mechanical coupling problems (Alkali-aggregate reactions, delayed ettringite reaction, decalcification, etc.). Each new phenomenon to be considered leads finite element code developers to question the best strategy to adopt to solve these increasingly complex mechanical-multiphysics problems. There is always a choice between a strongly coupled implementation of all the equations, requiring significant development time, or a segregation of the physics requiring less implementation time but more computation time to ensure compatibility of the equations via an iterative algorithm. The aim of our work is to propose criteria for choosing between these two strategies. The article recalls the algorithms of the methods and provides an illustration allowing its effectiveness to be verified through a comparison between the solution of a classic linear poromechanics problem obtained by a fully coupled method and the solution of this same problem obtained by a segregated algorithm. The interest of this classical example lies in the fact that the fully coupled formulation of the problem is linear, whereas it is non-linear in a segregated context. This case study permits to have an exact reference numerical solution of the coupled problem, and simultaneously a main problem with a non-linear segregated sub-problem to test the segregated algorithm numerically. The article concludes with a discussion of the drawbacks and advantages of the segregated method, both in terms of implementation time and computation time.