A　plastic　damage　model　with　the　non-orthogonal　flow　rule　is　developed,　which　is　consisted　of　the　damage　part　driven　by　plastic　strain　and　the　plastic　part　based　on　effective　stress.　In　the　damage　characterization,　the　degeneration　law　of　elastic　stiffness　is　described　by　the　damage　variable　in　the　form　of　exponential　function.　In　the　plastic　characterization,　the　evolution　for　plastic　strain　increment　(PSI)　is　characterized　from　the　magnitude　and　direction　perspective.　The　direction　of　PSI　is　obtained　directly　by　the　fractional　gradient　of　yield　surface　and　the　need　for　the　construction　of　plastic　potential　function　is　bypassed.　The　magnitude　of　PSI　is　calculated　based　on　the　effective　hardening　function　and　the　yield　function,　where　the　effective　hardening　function　corresponding　to　the　undamaged　material　is　derived　by　both　the　normal　hardening/softening　function　corresponding　to　the　damaged　material　and　the　damage　variable.　The　Next　Increment　Corrects　Error　(NICE)　algorithm　integrating　the　computational　accuracy　and　efficiency　is　used　for　the　numerical　implementation　of　model.　The　ability　of　model　to　capture　the　complex　mechanical　behavior　of　concrete　is　assessed　by　the　monotonous　and　cyclic　test　data　from　the　literature.　(C)　2019　Elsevier　B.V.　All　rights　reserved.