An approach to combining 3D discrete and finite element methods based on penalty function method

Abstract

An algorithm combining three-dimensional (3D) discrete and finite element methods is proposed. This new approach is conducted by decomposing the calculation domain into a finite element (FE) calculation domain and a discrete element (DE) calculation domain; the interaction between the two sub-domains is processed by using a penalty function method. Following the established model that combines spherical DEs and FEs, the corresponding numerical code is developed. The vibration process of two cantilever beams under dynamic force is simulated. By comparing the results calculated with different penalty factors set and also with that calculated by the finite element code LS-DYNA, it is found that the calculated results are unanimous and the precision is almost the same as LS-DYNA, as long as the penalty factor is large enough. Moreover, the vibration processes of two plates under impact of rigid spheres are simulated and the accuracy of the model proposed in this paper is further proved in the field of contact mechanics by comparing the simulating results with that calculated by using LS-DYNA. Finally, the impact fracture behavior of a laminated glass plate is simulated, with the influence of model parameters taken into consideration. And the numerical experiments show that the combined model can be used to predict some macroscopical physical quantities, such as the impact force of impactor.

Numerical Analysis of Impact Fracture of Laminated Glass - A Review

“…Fig. 17 shows the glass plies discretized into a series of DEs and the inter-layer discretized into a series of FEs [63]. Xu & Zang [35] developed four-point combined FE/ discrete element (DE) algorithm for the brittle fracture study of the LG.…”

“…Fig. 17 shows the glass plies discretized into a series of DEs and the inter-layer discretized into a series of FEs [63]. …”

A coupled distinct lattice spring model for rock failure under dynamic loads

“…In these models, the microscopic model is the particle based discrete model and the macroscopic continuum model utilized is typically the Finite Element Method (FEM) e.g. [16][17][18][19][20]. The coupling of the Discrete Element Method (DEM) and the FEM emerged in the late 1980s and several different models were proposed, e.g.…”

“…12.006 between the FEM block domain and particles around the interface. For example, Onate and Rojek [16] developed a contact algorithm in their model, Yan et al [17] used the ghost particle method, Lei and Zang [20] used a penalty function method and Elmekati and Shamy [18] and Cai et al [24] used the contact function provided in commercial codes to undertake a coupled analysis of geotechnical systems. Another recently developed approach is the use of a bridging domain to link two different scale models [19]; this coupling technique is called the bridging domain method, which was first developed by Xiao and Belytschko [25] for coupling Molecular Dynamics (MD) and FEM.…”

“…Moreover, in most coupled models (e.g. [16][17][18][19][20]), the microscopic and macroscopic domains remain unchanged during the computational process and transition from macroscopic level to microscopic model is not considered.…”