The　numerical　implementation　of　advanced　plastic　damage　models　has　been　challenging　due　to　the　diverse　computational　difficulties　caused　by　material　nonlinearity.　In　this　study,　firstly,　a　plastic　damage　model　is　developed　by　a　nonsmoothed　Mohr-Coulomb　yield　criterion.　The　nonorthogonal　flow　rule　without　plastic　potential　function　is　employed　to　describe　the　dilatancy　behavior　of　concrete.　The　stiffness　degradation　is　considered　through　two　tensile　and　compressive　damage　variables.　Subsequently,　an　implicit　stress　update　algorithm　incorporating　several　advanced　numerical　methods　is　proposed　to　tackle　difficulties　arising　in　the　numerical　calculation　of　the　plastic　damage　model.　In　the　model　implementation,　the　Mohr-Coulomb　yield　function　with　corners　is　replaced　by　a　single　smooth　expression　to　ensure　the　stability　of　the　numerical　calculation.　A　line　search　method　is　used　to　solve　nonlinear　systems　of　integral　stress　equations　to　obtain　better　convergence　than　Newton　method.　The　complex　step　derivative　approximation　is　used　to　evaluate　the　consistent　tangent　operator　to　provide　quadratic　convergence　speed　of　the　global　equilibrium　iterations,　thus　avoiding　tedious　analytical　derivative　operations.　The　integral　nonlocal　method　is　also　used　to　regularize　the　finite　element　solution.　At　the　material　point　scale,　the　ability　of　the　proposed　model　to　describe　the　complex　mechanical　behavior　of　concrete　is　verified　by　utilizing　nine　sets　of　monotonic　and　cyclic　loading　and　unloading　tests.　Finally,　the　algorithm　and　model＇s　performance　is　well　tested　by　the　failure　analysis　of　five　numerical　examples.　The　code　of　this　work　will　be　freely　available　at　https://github.com/zhouxin615/PD_model.　&　COPY;　2023　Elsevier　B.V.　All　rights　reserved.