A viscoelastic Mooney–Rivlin model for adhesive curing and first steps toward its calibration based on photoelasticity measurements

Abstract

AbstractThe transition of polymer adhesives from an initially liquid to a fully cured viscoelastic state is accompanied by three phenomenological effects, namely an increase in stiffness and viscosity in conjunction with a decrease in volume (curing shrinkage). Under consideration of these phenomena, some of us (Hossain et al. in Computational Mechanics 46:363-375, 2010) have devised a generic, viscoelastic finite strain framework for the simulation of the curing process of adhesives, which renders a thermodynamically consistent model regardless of the selected free energy density. In the present work, this generic curing framework is modified by means of more precise integration schemes and is applied to a hyperelastic Mooney–Rivlin material based on an additive volumetric-isochoric split of the strain energy density. The benefit of this decomposition is directly related to the distinct material responses of various polymers to volumetric and isochoric deformations [4]. The resulting Mooney–Rivlin curing model provides the foundation for implementing a user-defined material subroutine (UMAT) in Abaqus requiring the Cauchy stress and a non-standard formulation of the tangent operator. To this end, the corresponding transformations are presented. Additionally, a first attempt to determine the evolution of the curing-dependent material parameters through optimization with respect to a photoelasticity measurement is presented. A subset of the material properties, which reflect the emergence of shrinkage stresses inside a ceramic-epoxy composite after its fabrication, is determined via inverse parameter identification. However, due to a lack of experimental data and some rather strong assumptions made on the physics involved, this demonstration can currently be considered only as a proof-of-concept.