Sequential parameter estimation of an Ogden-hyperfoam model with Mullins damage for expanded polystyrene under cyclic compression

The cyclic compressive response of expanded polystyrene foams exhibits stress softening, hysteresis, and progressive cycle-to-cycle degradation of peak stress. This work presents a sequential framework for parameter estimation of an interpretable constitutive model: an Ogden–hyperfoam potential coupled with an Ogden–Roxburgh pseudo-elastic Mullins damage function and a cumulative degradation factor driven by the accumulated stretch path. The eight parameters are estimated with an Unscented Kalman Filter under a phase-gating scheme: the hyperelastic parameters are updated exclusively on the virgin loading branch and the damage parameters exclusively during unloading and reloading. The damage internal variables are purely kinematic, so the identified model generates the full stress sequence from the stretch history alone. Evaluated in this replay mode against uniaxial cyclic compression experiments on two foam densities (24.0 and 8.5 kg/m 3 ), with identical settings and initialization, the identified models attained R 2 = 0.956 and R 2 = 0.990 over ten loading–unloading cycles, reaching 98.5 % and 99.4 % of the accuracy of the best nonlinear least-squares fit of the same model. In a walk-forward test, parameters frozen at the end of each cycle predicted the next, unseen cycle with R 2 ≥ 0.96 from the second cycle onward. The shear moduli estimated by nonlinear least squares scale with density as μ ∝ ρ 1.85 and those estimated sequentially as μ ∝ ρ 1.43 , both within the interval spanned by the classical Gibson–Ashby laws, and the compressibility exponent converges toward zero, consistent with the near-zero Poisson ratio of expanded polystyrene. The framework combines the interpretability of classical pseudo-elasticity with the efficiency of sequential estimation.