The determination of the curing induced, nonlinear elastic field of an inclusion in photo-cured materials

Abstract

A wide variety of photo-cured materials have recently been developed with the rapid advancement of three-dimensional (3D) printing technology. However, most of these materials are designed as soft functional materials, and their failure mechanisms have received little attention. This work studies the mesoscale residual stress defects of photo-cured materials that are generated due to non-uniform curing and volume shrinkage during the manufacturing process. The defects are simplified as uncured inclusions embedded within a fully cured, infinite matrix which are then additionally cured. A large deformation model, validated against finite element analysis, is established to determine the nonlinear elastic field induced by the curing of inclusions with different Poisson’s ratio and shape (i.e., sphere and prolate spheroid), and is shown to outperform the infinitesimal strain model. This large deformation model, which includes a phase evolution constitutive model to describe the inclusion’s behavior and a compressible neo-Hookean model to describe the matrix’s behavior, is derived based on the same elastic field distribution as that in the infinitesimal strain solution and an ellipsoid-ellipsoid transformation kinematics assumption. The final solution is expressed in a discrete formulation and is exact for the spherical inclusion and approximate for the prolate spheroid inclusion. The prediction results of the theoretical model are compared with the finite element analysis, and reasonable agreement is obtained. This study may lay a foundation for investigating the effects of mesoscale residual stress defects on the mechanical behavior of 3D printing materials.