Emami, M.M., Jamshidian, M., Rosen, D.W., “Multiphysics modeling and experiments of grayscale photopolymerization with application to microlens fabrication,” Journal of Manufacturing Science and Engineering, Vol. 143, paper 091005, Sept. 2021.  DOI: 10.1115/1.4050549


A phenomenological model of a single-shot grayscale photopolymerization process is developed and used within a virtual process planning framework for microlens fabrication. Along with previous research, the kinetic relations describing the solidification of UV-curable resin are derived based on the underlying chemical reactions involved in free radical photopolymerization. As enhancements to the state-of-the-art, our multiphysics model includes a recently proposed super-Gaussian description of the light field, as well as the photobleaching effect due to the live reduction in photoinitiator concentration during UV illumination. In addition, heat generation and thermal strains due to the exothermic chemical reactions, and chemical shrinkage due to polymerization and cross-linking of monomers are considered. The model is numerically implemented via finite element method in comsol multiphysics software. Using a simulation-based virtual process planning framework, customized microlenses are fabricated with an in-house grayscale lithography experimental setup for digital micromirror device (DMD)-based volumetric additive manufacturing. Simulation and experimental results show that after the end of exposure, the temperature quickly rises by the advancement of exothermic chemical reactions and reaches a maximum rise of 100 K in a few seconds, followed by a slow cooling and recovery of thermal strains. It is observed that chemical and thermal shrinkages can compromise the dimensional accuracy of the final part near the resin–substrate interface due to the strong adhesion of the solidified part to the rigid substrate that prevents material shrinkage in the vicinity of the rigid substrate.


photopolymerization, grayscale lithography, multiphysics modeling, microlens fabrication, additive manufacturing, modeling and simulation, rapid prototyping and solid freeform fabrication

The effect of photobleaching on the microlens profile is shown by comparing simulation results with and without photobleaching effect