Rubber　is　a　key　component　of　military　equipment　in　aerospace　and　large　ships.　Stress　softening,　hysteresis,　and　cyclic　softening　occur　because　hyperelastic　bodies　undergo　large　deformations,　which　directly　affect　national　defense　security　and　livelihood.　In　this　work,　a　batch　of　dumbbell　IA　rubber　specimens　were　designed　for　different　vulcanization　processes,　and　quasi-static　uniaxial　tensile　and　cyclic　unloading　experiments　were　completed　to　study　the　influence　of　different　degrees　of　hardness　on　rubber　stress　softening.　The　least-squares　method　was　used　to　fit　the　experimental　data　and　obtain　the　Mullins　effect　(stress　softening)　to　induce　directional　damage　parameters.　The　stress-softening　rule　of　different　material　constitutions　was　analyzed　by　introducing　the　damage　parameters　into　the　ANSYS　software　program.　The　results　showed　that　the　greater　the　degree　of　hardness,　the　more　obvious　is　the　stress　softening　during　the　first　loading　and　unloading.　Under　the　pseudo-elastic　theory,　the　simulation　results　of　neo-Hookean　and　Mooney-Rivlin　(M-R)　material　constitutive　specimens　all　met　the　requirements　and　were　in　good　agreement　with　the　experimental　results　when　0　＜　lambda　1.　The　simulation　accuracy　of　the　M-R　constitutive　model　was　more　accurate　and　in　good　agreement　with　the　experimental　results　when　lambda　＞　1.