Partitioned Strong Coupling of Discrete Elements with Large Deformation Structural Finite Elements to Model Impact on Highly Flexible Tension Structures

Abstract

This article presents a staggered approach to couple the interaction of very flexible tension structures with large deformations, described with the finite element method (FEM), and objects undergoing large, complex, and arbitrary motions discretized with particle methods, in this case the discrete element method (DEM). The quantitative solution quality and convergence rate of this partitioned approach is highly time step dependent. Thus, the strong coupling approach is presented here, where the convergence is achieved in an iterative manner within each time step. This approach helps increase the time step size significantly, decreases the overall computational costs, and improves the numerical stability. Moreover, the proposed algorithm enables the application of two independent, standalone codes for simulating DEM and structural FEM as blackbox solvers. Systematic evaluations of the newly proposed iterative coupling scheme with respect to accuracy, robustness, and efficiency as well as cross comparisons between strong and weak FEM-DEM coupling approaches are performed. Additionally, the approach is validated against the rest position of an impacting object, and further examples with objects impacting highly flexible protection structures are presented. Here, the protection nets are described with nonlinear structural finite elements and the impacting objects as DEM elements. To allow the interested reader to independently reproduce the results, detailed code and algorithm descriptions are included in the appendix.

Influence of DE-cluster refinement on numerical analysis of rockfall experiments

“…In particular, [5][6][7] describe the possibility to apply the aforementioned coupling to analyse rockfall events modelling the interaction of the rock with the ground. Recently [8,9] used the FEM to calculate the highly nonlinear structural response of protection nets to the extreme load cases of rockfall events (simulated by the DEM), allowing for a deeper understanding of the interaction of impacting objects with flexible tension structures. Nevertheless, for the sake of completeness, a short introduction is given in the proceeding subsections expressing tensors with bold letters and scalar values with regular letters.…”

“…2. The respective normal, tangent spring stiffness k n , k t as well as the normal, and tangent damping coefficients c n , c t are used to calculate the contact forces [9,15,[21][22][23]. To restrict the maximum tangential force to the Coulomb's friction limit the coefficient of friction μ is applied.…”

“…The coupling procedure is described in detail in [8,9]. The basic idea is the exchange of data between two stand-alone analyses.…”

“…Recently, the work of [8,9] explained how to realize a multi-physics analysis of rock impact in an open-source code. The code that is used within this work is KRATOS [10][11][12][13].…”

“…-Section 2 briefly describes the underlying coupling theory and the respective components in this multi-physics simulation (see [8,9] for detailed information). -Section 3 describes the experiment which will be used for validation and calibration.…”