FEMxDEM multiscale modeling: model performance enhancement, from Newton strategy to element loop parallelization

This paper presents a multiscale model based on a FEM×DEM approach, a method that couples discrete elements at the microscale and finite elements at the macroscale. FEM×DEM has proven to be an effective way to treat real-scale engineering problems by embedding constitutive laws numerically obtained using discrete elements into a standard finite element framework. This proposed paper focuses on some numerical open issues of the method. Given the nonlinearity of the problem, Newton's method is required. The standard full Newton method is modified by adopting operators different from the consistent tangent matrix and by developing ad-hoc solution strategies. The efficiency of several existing operators is compared, and a new and original strategy is proposed, which is shown to be numerically more efficient than the existing propositions. Furthermore, a shared memory parallelization framework using OpenMP directives is introduced. The combination of these enhancements allows to overcome the FEM×DEM computational limitations, thus making the approach competitive with classical FEM in terms of stability and computational cost.