Global yield surface construction of polymethacrylimide foam by an integrated approach combining nanoindentation, machine learning and microstructure-informed modeling

Polymethacrylimide (PMI) foam is extensively utilized in lightweight sandwich structures yet lacks a reliable global yield surface for design guidance. This study presents an integrated experimental-computational framework for PMI foam yield surface construction. Cell-wall properties were precisely determined via nanoindentation combined with an inverse identification approach employing finite element modeling, machine learning, and traversal algorithms. A microstructure-informed Voronoi model, generated from micro-CT data and incorporating gas-filled cells with cell-wall properties, was developed for PMI foam simulation. Following validation against experimental uniaxial stress–strain curves, the model was subjected to multiaxial simulations under varying loading ratios to acquire comprehensive yield points for global yield surface construction, which was verified by equivalent biaxial tensile/compressive tests. The results show the cell-wall possesses 10.49 % higher Young’s modulus and 8.00 % greater initial yield stress than PMI matrix. Uniaxial microstructural analysis reveals intracellular gas enhances compressive strength by 6.33 % while minimally affecting tensile behavior. Notably, the yield surface shows distinct tension–compression asymmetry in stress/strain plane, near-perfect ellipsoidal fitting (R2 = 0.998) in principal strain space, and excellent predictive accuracy with equivalent biaxial test errors of −4.06 % (tension) and + 9.85 % (compression). These results provide theoretical foundations for safety optimization and structural design of PMI foam in engineering applications.