The　finite　element　method　(FEM)　is　an　effective　approach　for　exploring　the　failure　mechanism　of　heterogeneous　materials.　According　to　the　complementary　energy　principle,　the　use　of　FEM　might　suffer　from　several　difficulties　in　terms　of　keeping　the　elements　and　their　boundaries　balanced,　as　well　as　finding　interpolation　functions.　In　this　study,　we　introduced　an　efficient　approach　to　researching　the　failure　mechanism　of　the　material,　named　base　force　element　method　(BFEM),　according　to　complementary　energy　principle.　Specifically,　the　element　compliance　matrix　of　an　arbitrary　quadrilateral　element　with　four　mid-edge　nodes　was　expressed　based　on　the　complementary　energy　principle.　Then,　the　node　displacement　was　obtained　by　the　governing　equation　using　the　Lagrange　multiplier　method.　In　addition,　both　the　compliance　matrix　and　the　node　displacement　were　represented　as　explicit　expressions　without　the　use　of　Gaussian　integration.　A　numerical　model　of　the　recycled　aggregate　concrete　(RAC)　was　established　according　to　the　Monte　Carlo　method.　A　comparative　sample　of　the　digital　image　model　was　also　established　using　digital　image　technology.　The　influences　of　substituting　recycled　aggregate　and　the　relative　mechanical　properties　of　adhered　mortar　to　those　of　new　mortar　on　the　failure　mechanism　of　RAC　were　studied.　The　simulation　results　indicated　that　the　BFEM　is　an　effective　approach　to　researching　the　damage　mechanism　of　heterogeneous　materials.