Data-Driven Multi-Material Finite Viscoelasticity via Neural ODE Evolution Laws with Application to 3D-Printed Materials
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Digital materials produced by multi-material 3D printing are engineered as controlled mixtures of glassy and rubbery base constituents, leading to strongly rate-dependent and dissipative mechanical responses. Classical finite-strain viscoelastic models are described by internal variables with prescribed evolution laws, allowing closed-form representation that limits flexibility over various materials and loading rates. We presented in this work a data-driven, multi-material generalization of the three-branch Bergström–Boyce framework where the evolution law is replaced by a neural ordinary differential equation (NODE) learning directly from data on how to evolve rate-dependently internal variables. Objective strain and strain rate invariants drive NODE which are further conditioned on a compact and continuous latent embedding of the material recipe, i.e., features such as hardness index as well as other formulation identifiers such as dye color. In this way, the same parameterization interpolates both across deformation regimes as well as across multiple materials. Using multi-rate uniaxial compression datasets, we calibrate the model jointly across materials. The NODE-based formulation accurately describes rate-dependent stiffness and hysteresis across materials while preserving thermodynamic consistency at the continuum level.
