To　address　the　indeterminacy　of　contacts　involving　nonconvex　angles　of　arbitrarily　shaped　polyhedron,　an　easy-to-implement　local　convex　decomposition　method(LCD),　dividing　any　arbitrary　angle　along　the　extensive　plane　angle　of　concave　dihedral　angles　into　a　set　of　convex　angles,　was　proposed　and　employed　to　extend　the　entrance　plane　method(EPM).　The　LCD-EPM　is　a　universal　method　for　contact　detection　of　general　polyhedrons,　and　herein,　enabled　the　use　of　a　three-dimensional　discontinuous　deformation　analysis　(3-D　DDA)　to　calculate　contacts　between　general　polyhedrons.　Finally,　the　extended　3-D　DDA　program　was　used　to　illustrate　the　powerful　ability　of　LCD　including　contact　detection　and　calculation　as　well　as　an　impact-contact　behaviour　analysis　of　general　polyhedrons,　which　validates　the　correctness　and　robustness　of　the　LCD-EPM.　The　extended　3-D　DDA　program　can　be　applied　in　mechanical　analyse　of　complex　polyhedral　block　systems.　©　2018,　Science　Press.　All　right　reserved.