The　partition　of　unity　based　methods,　such　as　the　extended　finite　element　method　and　the　numerical　manifold　method,　are　able　to　construct　global　functions　that　accurately　reflect　local　behaviors　through　introducing　locally　defined　basis　functions　beyond　polynomials.　In　the　dynamic　analysis　of　cracked　bodies　using　an　explicit　time　integration　algorithm,　as　a　result,　huge　difficulties　arise　in　deriving　lumped　mass　matrices　because　of　the　presence　of　those　physically　meaningless　degrees　of　freedom　associated　with　those　locally　defined　functions.　Observing　no　spatial　derivatives　of　trial　or　test　functions　exist　in　the　virtual　work　of　inertia　force,　we　approximate　the　virtual　work　of　inertia　force　in　a　coarser　manner　than　the　virtual　work　of　stresses,　where　we　inversely　utilize　the　＇from　local　to　global＇　skill.　The　proposed　lumped　mass　matrix　is　strictly　diagonal　and　can　yield　the　results　in　agreement　with　the　consistent　mass　matrix,　but　has　more　excellent　dynamic　property　than　the　latter.　Meanwhile,　the　critical　time　step　of　the　numerical　manifold　method　equipped　with　an　explicit　time　integration　scheme　and　the　proposed　mass　lumping　scheme　does　not　decrease　even　if　the　crack　in　study　approaches　the　mesh　nodes-a　very　excellent　dynamic　property.　Copyright　(C)　2017　John　Wiley　&　Sons,　Ltd.