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

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.