A virtual-surface contact algorithm for the interaction between FE and spherical DE

A new contact search algorithm named virtual-surface contact algorithm is developed for dealing with the interaction between spherical discrete elements (DEs) and finite elements (FEs). The basic idea of the contact algorithm is forming a virtual surface above the FE surface. Therefore, the contact problem between DE and FE surface is treated as that between the DE mass center and the virtual surface. Then, the projection of the DE mass center on the virtual surface is determined using spatial area coordinates without solving nonlinear equations and the contact force is processed by using a penalty function method. So, the quick contact searching and accurate evaluation of penetration have been achieved. Finally, the accuracy of this algorithm is investigated via four numerical examples. •The virtual-surface contact algorithm, which is based on inside–outside method and penalty function method, is developed. Innermost details regarding local search, contact force calculation and the algorithmic implementations are presented.•In the proposed contact algorithm, the penetration between discrete element and finite element can be determined without solving nonlinear equations.•The proposed contact algorithm has been implemented into in-house developed code. Four numerical examples are employed to validate the accuracy and robustness of the proposed contact algorithm.