A　two-dimensional　micro-nano　grinding　model　with　the　fractal　surface　is　constructed,　which　considers　the　wear-out　failures　of　the　materials　and　the　adhesive　effects　in　the　contact　process.　Also,　the　strain　changes　of　the　asperity　during　the　grinding　are　dynamically　discussed.　The　finite　element　method　is　employed　to　simulate　the　strain　field　in　the　process　of　grinding.　It　is　indicated　that　the　larger　the　interfacial　shear　strength　is,　at　the　same　grinding　distance,　the　greater　its　equivalent　plastic　strain　is,　the　easier　the　rough　solid　is　prone　to　wear　and　tear.　The　maximum　point　of　the　plastic　deformation　determines　the　first　place　where　the　first　cracks　occur,　either　on　the　surface　or　at　a　certain　distance　from　the　surface.　Also,　the　larger　the　normal　even-distributed　load　is,　the　larger　the　maximum　plastic　deformation　of　the　asperity　at　the　initial　contact　time　is,　which　determines　an　earlier　occurrence　time　of　the　initial　cracks.　Furthermore,　the　greater　the　grinding　rate　is,　the　longer　the　distance　that　two　interactively　contacting　asperities　start　to　wear　is.　By　studying　the　distribution　of　the　strain　field　of　the　embedded　asperities,　the　real　causes　why　the　materials　are　ground　and　worn　at　the　scale　of　micro-nano　are　explored.