As　a　novel　material　that　integrates　structural　properties　and　functions,　functional　gradient　metal　rubber　(FGMR)　has　extensive　application　prospects　due　to　its　lightweight,　thermal　protection,　and　vibration-damping　properties.　Of　particular　interest　and　complexity　is　the　unclear　relationship　between　the　gradient　configuration　and　hysteresis　characteristics,　owing　to　the　unique　internal　structure　of　FGMR.　In　this　work,　the　relationship　between　pore　characteristics　and　the　internal　structure　of　FGMR　was　investigated　using　a　gradient　equation　derived　from　image　processing,　which　incorporates　CT　scanning　and　threshold　segmentation　techniques.　Based　on　this,　a　constitutive　model　was　constructed　and　validated　through　quasi-static　and　dynamic　compression　experiments.　The　results　demonstrate　that　a　gradient　equation　can　effectively　represent　the　relationship　between　the　density　and　structure.　The　gradient　configuration　has　a　significant　influence　on　the　compressive　performance　of　FGMR.　High　prediction　accuracy　of　the　constitutive　modeling　for　the　FGMR　is　exhibited.　©　2025　Elsevier　Ltd