On the strain-rate sensitivity of 3D-printed hyper-viscoelastic polymers

Purpose Additive manufacturing has promoted the use of polymeric materials with complex mechanical behavior, including thermoplastic polyurethanes (TPUs). These materials exhibit pronounced nonlinear and strain-rate-dependent responses that remain insufficiently characterized for constitutive modeling. This study aims to experimentally characterize the strain-rate-dependent tensile behavior of printable TPUs. It evaluates, adapts, and implements phenomenological constitutive models to describe their hyper-viscoelastic response over a relevant strain-rate range and demonstrates their applicability through finite-element implementation. Design/methodology/approach Uniaxial tensile tests were performed on three printable TPU grades (Shore 70A, 82A and 95A) at four nominal strain rates ranging from approximately 1.1 × 10-3 s-1 to 10-1 s-1. The experimental stress–strain data were used to assess two phenomenological modeling approaches: a modified Cowper–Symonds formulation incorporating strain-dependent rate sensitivity along the full stress–strain response and an integrated hyper-viscoelastic framework combining a third-order Ogden model with a Prony series to represent time-dependent effects. The integrated formulation was further implemented in a commercial finite element environment using a representative gait-related loading scenario. Findings Both modeling approaches reproduce the experimentally observed strain-rate-dependent stress–strain behavior with high accuracy within the investigated range. Residual analysis indicates that the modified Cowper–Symonds formulation yields low root-mean-square errors (RMSEs), with a maximum of approximately 0.21 MPa. In contrast, the integrated hyper-viscoelastic framework exhibits RMSE values below approximately 0.35 MPa. In all cases, the agreement between modeled and experimental responses is characterized by coefficients of determination (R²) exceeding 0.99. The remaining discrepancies are mainly due to limitations in the relaxation data and numerical integration effects, which become more pronounced at higher strain rates. Finite element simulations slightly overestimate experimental stress levels, consistent with the reported RMSE values and attributable to differences in adequate integration time. Originality/value This study contributes to the analytical and numerical modeling of 3D-printed TPUs and other compliant, printable polymers by establishing an experimentally grounded framework for selecting, adapting, and implementing constitutive models. Validated hyperelastic and viscoelastic descriptions are systematically integrated with strain-rate-dependent experimental data and finite element simulations, enhancing the predictive reliability of TPU-based designs and supporting their application in advanced structural and biomechanical contexts.