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.

A numerical analysis is validated against a Swiss Federal Commission for Technology and Innovation (CTI)—frame impact experiment conducted by the Swiss Company Geobrugg. The discrete element method is used to simulate the impacting object, while the highly nonlinear structural response is analysed with the finite element method. Both methods are coupled within an open-source multi-physics research code to exchange data and simulate the interaction. The successful practical application of the coupling algorithm is demonstrated with this work, as the numerical results show good agreement with the experimental results. Within this paper the main focus is the appropriate modelling of the impacting objects, which heavily influences the simulation results, while a simplified structural model allows a correct assessment of the global deformation behaviour and reaction forces.

Attenuator barriers, in contrast to conventional safety nets, tend to smoothly guide impacting rocks instead of absorbing large amounts of strain energy arresting them. It has been shown that the rock’s rotation plays an important role in the bearing capacity of these systems. Although experimental tests have to be conducted to gain a detailed insight into the behavior of both the structures and the rock itself, these tests are usually costly, time-consuming, and offer limited generalizability to other structure/environment combinations. Thus, in order to support the engineer’s design decision, reinforce test results and confidently predict barrier performance beyond experimental configurations this work describes an appropriate numerical modeling and simulation method of this coupled problem. For this purpose, the Discrete Element Method (DEM) and the Finite Element Method (FEM) are coupled in an open-source multi-physics code. In order to flexibly model rocks of any shape, sphere clusters are used which employ simple and efficient contact algorithms despite arbitrarily complicated shapes. A general summary of the FEM formulation is presented as well as detailed derivations of finite elements particularly pertinent to rockfall simulations. The presented modeling and coupling method is validated against experimental testing conducted by the company Geobrugg. Good agreement is achieved between the simulated and experimental results, demonstrating the successful practical application of the proposed method.

No abstract

No abstract