A 3-D discrete element method is presented on the basis of new definition of distance potential function

which is suitable for the arbitrary polyhedral elements. In this approach

the potential function is characterized as a distance function between the contacts using a normalized computational algorithm. Meanwhile

the calculation formulations for contact interaction are deduced with the new function. Thus this new distance potential function implies sound physical meaning

and is reasonable and concise to avoid different contact situations. This method overcomes the problems of the original potential method in which the physical meaning of potential function is not clear and the calculation of contact force is affected by the element form. Furthermore

it gets rid of the restrain of tetrahedral shape and can be applied to arbitrary polyhedrons. Several examples are analyzed to demonstrate the accuracy and efficiency of this new method. This method shows good capability of handling the problem of contact transformation for arbitrary polyhedrons and the motion process of the complex discontinuous media.