Observable history interactions in path-dependent plasticity: response-space estimability and constitutive architecture discrimination

Sequential loading in metals can produce indistinguishable lower-order responses while leaving non-additive components of the subsequent constitutive response unresolved. This study develops a response-space framework for determining which history interactions are directly observable from a prescribed set of loading histories. For an arbitrary incomplete programme, a target interaction is exactly estimable when every response cell in its unique matched-history representation is observed; a pure order- m interaction therefore requires the corresponding 2 m matched subhistories. Parameter directions acting only through missing interactions are locally unidentifiable, while interaction sensitivities and covariance quantify the information content of admissible loading paths. A controlled fading-memory model demonstrates lower-order equivalence, joint-history rank recovery and path-dependent parameter informativeness. Calculations with the Homogeneous Anisotropic Hardening model (HAH-14) and the Homogeneous EXtended Anisotropic Hardening (HEXAH) framework identify a finite path-angle region in which lower-order responses agree while joint histories discriminate the constitutive architectures. Published copper experiments give complete matched pair interactions of −7.86 and −7.24 percentage points without interpolation, while reconstructed AA3103 histories give −2.2 to −4.8 percentage points across three amplitudes. The results establish matched sequential histories as quantitative observables for determining what a loading programme can identify about history-dependent constitutive response and for discriminating constitutive architectures that remain equivalent under lower-order loading.