The　full　response　of　a　brittle　structure　containing　multiple　cracks　to　loading　under　the　servo　control　is　of　vital　importance　in　the　evaluation　of　properties　of　the　structure.　During　crack　growth,　the　fracture　toughness　condition　at　all　the　crack　tips　as　well　as　the　equilibrium　condition　should　be　obeyed,　leading　to　a　nonlinear　complementarity　problem　(NCP).　The　vector-valued　function　in　the　NCP　depends　implicitly　on　the　cracking　increments　which　in　turn　determine　the　stress　field.　The　stress　field　can　be　obtained　through　solving　a　mixed　variational　problem.　Since　the　degrees　of　freedom　in　the　discrete　variational　problem　vary　with　cracking　not　only　in　magnitude　but　also　in　number,　the　Jacobian　matrix　of　the　NCP　is　hard　to　compute　and,　it　cannot　be　expected　to　be　solved　by　the　Newton　methods　that　involve　the　calculation　of　Jacobian　matrices.　Therefore,　a　well-scaled　projection-contraction　algorithm　is　designed.　The　proposed　procedure　is　able　to　simulate　growth　of　multiple　cracks　in　a　natural　way,　allowing　the　crack　tips　to　stop　anywhere　with　no　sensitivity　to　node　configuration　or　cracking　increments.　Through　the　analysis　of　some　examples　that　have　been　widely　tested,　many　interesting　and　profound　phenomena　are　found　which　have　never　been　revealed.　(C)　2015　Elsevier　B.V.　All　rights　reserved.