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Streszczenie:
This paper presents an extension of the authors’ previously developed interface coupling technique for 2D problems to 3D problems. The method combines the strengths of the Discrete Element Method (DEM), known for its adeptness in capturing discontinuities and non-linearities at the microscale, and the Boundary Element Method (BEM), known for its efficiency in modelling wave propagation within infinite domains. The 3D formulation is based on spherical discrete elements and bilinear quadrilateral boundary elements. The innovative coupling methodology overcomes a critical limitation by enabling the representation of discontinuities within infinite domains, a pivotal development for large-scale dynamic problems. The paper systematically addresses challenges, with a focus on interface compatibility, showcasing the method’s accuracy through benchmark validation on a finite rod and infinite spherical cavity. Finally, a model of a column embedded into the ground illustrates the versatility of the approach in handling complex scenarios with multiple domains. This innovative coupling approach represents a significant leap in the integration of DEM and BEM for 3D problems and opens avenues for tackling complex and realistic problems in various scientific and engineering domains.

Słowa kluczowe:
Interface coupling, Concurrent multi-scale coupling, Boundary element method (BEM), Discrete element method (DEM) , Staggered time integration, Dynamic wave propagation, Infinite domain

Streszczenie:
This paper presents a novel and highly efficient approach for coupling the Discrete Element Method (DEM) and the Boundary Element Method (BEM) for time-domain simulations of dynamic problems, utilising multi-scale staggered time integration. While the DEM captures phenomena with discontinuous behaviours, such as fracturing and granular flow, the BEM excels in accurately modelling seismic wave propagation in infinite domains. By separately solving the governing equations of the DEM and BEM at different time instants, the proposed scheme considerably enhances computational efficiency compared to conventional monolithic coupling schemes. The incorporation of non-conforming interfaces enables larger time steps in the BEM, thereby reducing computational costs and memory usage. Moreover, an innovative coupling of DEM rotations with the BEM displacement field is introduced, leading to more accurate and realistic modelling of complex dynamics. Numerical experiments are conducted to demonstrate the superior accuracy and efficiency of the proposed method, establishing its potential for modelling a wide range of dynamic problems.

Słowa kluczowe:
BEM-DEM coupling,Multi-scale time integration,Rotational degrees of freedom,Seismic wave propagation,Infinite domain

Streszczenie:
This work presents a novel scheme to couple the Boundary Element Method (BEM) and the Discrete Element Method (DEM) in the time domain. The DEM captures discontinuous material behaviour, such as fractured and granular media. However, applying the method to real-life applications embedded into infinite domains is challenging. The authors propose a solution to this challenge by coupling the DEM with the BEM. The capability of the BEM to model infinite domains accurately and efficiently, without the need for numerical artifices, makes it the perfect complement to the DEM. This study proposes a direct monolithic interface-based coupling method that resolves any incompatibilities between the two methods in two dimensions. The benchmark results show that the proposed methodology consistently produces results that align with analytical solutions. The final example in the paper showcases the full potential of this innovative methodology, where the DEM models a fracturing process, and the BEM evaluates its far-field effect.

Słowa kluczowe:
Discrete Element Method (DEM), Boundary Element Method (BEM), Discontinuous materials, Wave propagation, Infinite domain, Monolithic coupling

Streszczenie:
The discrete element method (DEM) is the most dominant method for the numerical prediction of dynamic behaviour at grain or particle scale. Nevertheless, due to its discontinuous nature, the DEM is inherently unable to describe microscopic features of individual bodies which can be considered as continuous bodies. To incorporate microscopic features, efficient numerical coupling of the DEM with a continuous method is generally necessary. Thus, a generalised multi-scale PD–DEM framework is developed in this work. In the developed framework, meshfree discretised Peridynamics (PD) is used to describe intra-particle forces within bodies to capture microscopic features. The inter-particle forces of rigid bodies are defined by the DEM whereas a hybrid approach is applied at the PD–DEM interface. In addition, a staggered multi-scale time integration scheme is formulated to allow for an efficient numerical treatment of both methods. Validation examples are presented and the applicability of the developed framework to capture the characteristics mixtures with rigid and deformable bodies is shown.

Słowa kluczowe:
Peridynamics (PD),Discrete element method (DEM),Contact coupling,Multi-scale modelling,Deformable particles

Streszczenie:
This work presents a novel scheme to couple the Discrete Element Method (DEM) and the Boundary Element Method (BEM) for the multi-scale modelling in the time domain. The DEM can model discontinuous material at micro scale very well, but it cannot represent infinite domains. Hence, coupling with the BEM is proposed. A formulation employing the DEM and BEM in different subdomains of the same body is presented. There is no overlap between the sub-domains, and the system of equations is derived based on strong equilibrium and compatibility conditions at the interface. The proposed coupling scheme is based on monolithic time integration. The conducted numerical experiments of one-dimensional wave propagation show excellent agreement with the analytical solution. Some spurious wave reflections are observed at the interface, but their effect is quantified and deemed not critical for infinite domains, which are of main interest. Even though the applications for one-dimensional wave propagation are of limited practical engineering interest, this work represents a significant theoretical breakthrough. This paper establishes a reference for future coupling schemes for two- and three-dimensional multi-scale analysis.

Słowa kluczowe:
siscrete element method (DEM), boundary element method (BEM), infinite domain coupling, dynamic multi-scale analysis, stability of time integration, spurious wave reflection

Streszczenie:
This work presents a 3D extension of the deformable discrete element method (DDEM) developed previously for 2D problems. The 3D formulation employs spherical particles. The particle deformation is made up of a global and local deformation mode. The global mode is assumed to be produced by uniform stress due to the contact forces. Particle deformability yields a nonlocal contact model, in which one contact between particles is influenced by contacts with other particles. It also leads to the formation of new contacts in the particle assembly. The DDEM affects the behavior of the granular material at the macroscopic level and gives new possibilities in material modeling by the discrete element method (DEM). The new algorithm is verified on a unconfined uniaxial compression test of a cuboid specimen discretized with equal‐size bonded particles aligned in a simple cubic pattern using an analytical solution. Enhanced modeling capabilities are presented by simulating cylindrical specimens discretized with a nonuniform size of bonded particles. The micro–macro relationships for elastic parameters are obtained. It is shown that the DDEM extends the range of the Poisson's ratio achievable with the DEM. Additional simulations are performed to determine the stability limits of the DDEM.

Słowa kluczowe:
average stress, deformable particles, discrete element method, elastic constants, micro–macro relationships, nonlocal contact model