Digital materials fabricated by multi-material 3D printing are designed as controlled mixtures of stiff and compliant constituents, yielding effective responses that span more than an order of magnitude in apparent stiffness and exhibit strongly nonlinear, composition‑dependent, and rate‑dependent dissipative behavior. Classical finite‑strain viscoelastic models represent such behavior with closed‑form strain‑energy functions for equilibrium and non‑equilibrium stresses together with internal‑variable evolution, which limits flexibility when a single constitutive model must generalize across materials and loading rates.
We present a data‑driven multi‑material constitutive modeling framework that generalizes the formulation of Bergström and Boyce. The framework retains the classical structure: multiplicative kinematics, invariant‑based strain‑energy functions, and a scalar dissipative evolution law directed along the normalized non‑equilibrium deviatoric stress.
For the equilibrium branch, the framework either directly predicts closed‑form model parameters as functions of composition or automatically constructs a polyconvex strain‑energy function using neural ordinary differential equations (NODEs). The non‑equilibrium branch kinetics are learned similarly, either by identifying closed‑form parameters across compositions or by employing appropriately constrained artificial neural networks.
Using multi‑rate uniaxial compression data across multiple material compositions, we demonstrate that the proposed formulation captures rate‑dependent stiffness and hysteresis across compositions while preserving thermodynamic consistency.
Review