Orienting　the　circular　and　rigid　particle　medium,　the　variational　inequality-based　discontinuous　deformation　analysis　(DDA)　is　established.　In　the　proposed　DDA,　the　global　stiffness　matrix,　the　penalty　parameters,　and　the　open-close　iteration　are　successfully　avoided.　The　contact　constraint　is　transferred　into　the　problem　of　variational　or　quasi-variational　inequalities.　And　explicit　variational　expression　on　the　contact　force　is　firstly　established.　To　speed　up　the　rate　of　solving　contact　force,　on　the　basis　of　the　two-stage　prediction-correction　method,　we　design　a　compatibility　iteration　algorithm　(PPC-CI).　The　C++　code　is　developed　in　multicore　environment　through　the　open　multi-processing　(OpenMP)　in　order　to　take　advantage　of　the　parallelizable　features　of　the　new　DDA.　Numerical　tests　suggest　that　the　presented　DDA　is　effective　and　promising.