A smooth contact algorithm for the combined finite discrete element method
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A smooth contact algorithm for the combined finite discrete element method Zhou Lei1 · Esteban Rougier1 · Bryan Euser1 · Antonio Munjiza2 Received: 8 November 2019 / Revised: 27 January 2020 / Accepted: 7 March 2020 © OWZ 2020
Abstract From its inception, the combined finite discrete element method has used a distributed potential contact force algorithm to resolve interaction between finite elements. The contact interaction algorithm relies on evaluation of the contact force potential field. The problem with existing algorithms is that the potential field introduces artificial numerical non-smoothness in the contact force. This work introduces a smooth potential field based on the finite element topology, and a generalized contact interaction law is constructed on top of the smooth potential field. A number of validation cases for the proposed algorithm, considering different shapes of discrete elements, are presented, and detailed aspects of the proposed contact interaction law are tested with numerical examples. Keywords Combined finite discrete element method · Finite element · Discrete element · Contact interaction · Contact potential field
1 Introduction Discrete element methods are effective tools for addressing a variety of physics problems and are formulated in terms of a large number of discrete entities interacting with each other, as opposed to treating the material as a continuum. In the combined finite discrete element method (FDEM) [1–5], solid domains (called discrete elements) are discretized into finite elements; the finite element discretization is used for calculating material deformation and resolving contact interaction between discrete elements. Utilizing this approach, discretized contact solutions can then be used for both contact detection and contact interaction. Additionally, these features can be coupled with discrete crack initiation and fracture propagation models. In this way, FDEM bridges the gap between finite element methods and discrete element methods. As such, it has become a method of choice for problems involving large material deformation, contact, fracture and fragmentation [6–21].
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Zhou Lei [email protected]
1
Geophysics Group, Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, NM 87545, USA
2
FGAG, University of Split, Split, Croatia
One advantage of FDEM is the ability to handle complex contact/impact problems, especially under dynamic loading. Figure 1 shows a typical problem that can be simulated using FDEM. In this case, a raster of deformable particles with irregular shapes are given some initial velocity and their resultant collisions are simulated. Each particle can freely move and rotate in space until it is in contact with other particles. As a result, random collisions take place between the particles. Due to the complexity of the contact problem, contact interaction algorithms for FDEM must be robust and easy to implement while maintaining high computational efficiency. Since the inception of FDEM, the potential-based penalty function method has b
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