Data-adaptive spline-based viscoelasticity for soft solids

Soft materials are typically characterized by finite deformations, nonlinear stress-strain behavior, and rate-dependent mechanical responses. To capture these features, we present Data-Adaptive Spline-Based Viscoelasticity (DAVIS), a computational framework for finite strain viscoelasticity. The approach builds on the theory of Reese and Govindjee and results in a data-adaptive generalized standard material formulation: the equilibrium and non-equilibrium energy functions and the dissipation potential are replaced by B-spline interpolants defined over invariant spaces. The splines are parameterized by interpolation values and an interpolation domain, the latter being automatically adapted using Kernel Density Estimation based on sampled invariant distributions. This strategy eliminates the need for manual domain specification, enabling a high degree of automation. The resulting parameter space is explored via Finite Element Model Updating in a two-stage calibration process: the equilibrium energy is identified first and held fixed during the subsequent calibration of the non-equilibrium energy and dissipation potential. Full-field displacement data and reaction forces from uniaxial tensile tests at various stretch rates serve as calibration input. We demonstrate the method on VHB Tape, a soft elastomer with pronounced rate-dependent behavior, showing that just two Maxwell elements—i.e., two non-equilibrium spline-based energy functions and dissipation potentials—suffice to accurately fit the full experimental dataset. Overall, Data-Adaptive Spline-Based Viscoelasticity is a flexible, constitutive-model-agnostic framework that can directly replace traditional constitutive models with data-driven splines—enabling seamless application across diverse rate-dependent material behavior. The computational framework is made openly available to facilitate future collaborative efforts in material modeling.