Data-Driven Constitutive Modeling for Multi-Material 3D-Printed Solids

Summary

Multi-material 3D-printed digital materials combine stiff and compliant constituents, producing apparent stiffness values that vary by more than an order of magnitude and showing nonlinear, composition-dependent, and rate-dependent dissipation. The paper presents a data-driven constitutive modeling framework that extends a Bergstrom-Boyce formulation. It preserves multiplicative kinematics, invariant-based strain-energy functions, and a scalar dissipative evolution law aligned with the normalized nonequilibrium deviatoric stress. For the equilibrium response, the method either learns closed-form parameters as functions of composition or constructs a polyconvex strain-energy function with neural ordinary differential equations. For nonequilibrium kinetics, it similarly identifies composition-dependent closed-form parameters or uses constrained artificial neural networks. Tests on multi-rate uniaxial compression data from several compositions show that the framework captures rate-dependent stiffness and hysteresis across the materials. The formulation also preserves thermodynamic consistency, addressing a central constraint in learned constitutive models.