Composition-dependent nonlinear viscoelastic-viscoplastic behavior and constitutive framework for digitally mixed polymers spanning the glass transition

Abstract

Multi-material PolyJet printing produces voxel-scale digital mixtures of an elastomeric photopolymer (Agilus) and a glassy photopolymer (Vero), giving a material family whose room-temperature response ranges from elastomeric to glassy; a unified description spanning the family has remained challenging. Large-deformation uniaxial compression over nearly three orders of magnitude in strain rate reveals a nonlinear, rate-dependent load-unload response that evolves continuously with composition, from recoverable elastomeric hysteresis to glassy yield with post-yield softening, hardening, and substantial residual strain. Dynamic mechanical analysis (DMA) shows that each mixture has a single glass transition temperature ($T_g$) that shifts to higher temperature with both Vero fraction and frequency, so composition acts much as temperature or loading rate does. This time-composition equivalence motivates one constitutive structure for the whole family rather than a separate property set per mixture: an equilibrium hyperelastic network with three non-equilibrium, rate-dependent branches carrying reptational, intermolecular, and glassy resistance. Its properties are anchored at the two endpoints and interpolated by smooth composition scaling laws. The model captures the compression response of all seven calibrated compositions and predicts a withheld mixture from the scaling laws alone. Resolving the predicted stress into its branches shows the load passing from the elastomeric to the glassy mechanism, and the work from elastic storage to dissipation, as Vero content and rate rise. The glass transition that DMA maps at small strain therefore governs the large-strain deformation mechanisms. The framework gives a compact, physically based description of digitally mixed polymers and a predictive basis for designing functionally graded, architected multi-material structures.