A multiscale framework for the elasto-plastic constitutive equations of crosslinked epoxy polymers considering the effects of temperature, strain rate, hydrostatic pressure, and crosslinking density

• Published in: Journal of the mechanics and physics of solids 2020-09, Vol.142, p.103962, Article 103962
• Main Authors: Park, Hyungbum, Cho, Maenghyo
• Format: Article
• Language: English
• Subjects: Argon; Combined loading; Computer simulation; Constitutive behavior; Constitutive equations; Constitutive models; Constitutive relationships; Continuum modeling; Crosslinking; Density; Finite element method; Finite elements; Hardening rate; Hydrostatic pressure; Laboratory tests; Mathematical models; Molecular dynamics; Multiscale analysis; Patch tests; Polymeric material; Polymers; Residual stress; Simulation; Strain rate; Structures; Temperature effects; Thermomechanical properties; Three dimensional models; Yield strength; Yield stress
• ISSN: 0022-5096; 1873-4782
• DOI: 10.1016/j.jmps.2020.103962

•Multiscale simulations are conducted to study plastic deformations of epoxy polymer considering timescale limitations of molecular dynamics.•Effects of strain rate, temperature, hydrostatic pressure, and crosslinking density are examined.•A cooperative model is adopted as a link between simulations and experiments for proper description of nonlinear characteristics of yielding.•Finite element analysis based on the paraboloidal yield surface is performed. In this study, a multiscale approach was constructed for the multi-axial plastic deformations of epoxy polymers to develop a macroscopic constitutive model at a quasi-static strain rate (consistent with laboratory tests) without any experiments. The 3-dimensional constitutive model was fully characterized, considering the effects of strain rate, temperature, hydrostatic pressure, and crosslinking density. The quasi-static yield stress was predicted by conducting molecular dynamics simulations based on the Argon theory and internal stress law established by thermomechanical properties. For the proper description of nonlinear dependences of the obtained yield stresses on the strain rate and temperature, which have not been considered in previous studies, a cooperative model was adopted as a link between the simulations and experiments. Taking into account characteristic quasi-static yield behavior, one-dimensional quasi-static constitutive equations were derived by developing hardening laws considering strain rate dependences of the yield strain and yield stress established at the quasi-static level. Finite element analysis was then performed on these equations considering the influence of temperature, hydrostatic pressure, and crosslinking density by implementing a continuum model based on the paraboloidal yield function. Finite element simulations included a 1-element patch test conducted for one-dimensional loading paths and open-hole test performed for both the validation and practical use of the model describing the structural behavior of the studied polymer under combined loading. The results of open-hole simulations revealed that the proposed multiscale framework successfully considered the microscopic structural characteristics of amorphous polymers in establishing elasto-plastic finite element models.