ED-VPINN: Physics-Embedded Constitutive Operator Learning for Aging-Dependent Viscoelastic Damage in Solid Propellants with Finite Element Implementation

Aged solid propellants exhibit coupled viscoelasticity, damage softening, and material-property degradation, which are difficult to represent accurately while retaining finite-element compatibility. Existing analytical viscoelastic-damage models are physically interpretable but often require extensive calibration and may lose robustness when aging-dependent softening and consistent tangents are introduced. This work proposes ED-VPINN, a parametric incremental constitutive operator learning framework for aged HTPB-based solid propellants. The framework embeds a generalized Maxwell model as a structural prior in an encoder–decoder backbone to learn parameterized viscoelastic stress increments and the corresponding algorithmic tangent. A hard-constrained softening network then maps the linear viscoelastic response to an aging-dependent damage-softened response while enforcing boundedness, monotonic softening, damage irreversibility, and non-negative dissipation within the calibrated uniaxial aging-tension domain. Validation proceeds at two levels: synthetic benchmarks using analytically prescribed relaxation responses, and uniaxial tensile tests on aged HTPB-based specimens. In the synthetic benchmarks, the Maxwell backbone reproduces theoretical viscoelastic responses over material parameters spanning four orders of magnitude, with an average relative error below 0.5%. In the experimental validation, ED-VPINN achieves a validation-set stress MRE of 2.404%. Compared with the Schapery damage model used as the baseline, it reduces the validation-set stress MRE from 5.077% to 2.404% and the stress MAE from 0.0475 MPa to 0.0171 MPa. The complete model is compiled into a UMAT and embedded in finite-element simulations of tensile specimens and selected tubular-motor hydraulic-shock cases, showing agreement with measurements within the tested loading range.