A finite strain framework for the simulation of polymer curing. Part I: elasticity
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A phenomenologically motivated small strain model to simulate the curing of thermosets has been developed and discussed in a recently published paper (Hossain et al. in Comput Mech 43(6):769–779, 2009). Inspired by the concepts used there, this follow-up contribution presents an extension towards the finite strain regime. The thermodynamically consistent framework proposed here for the simulation of curing polymers particularly is independent of the choice of the free energy density, i.e. any phenomenological or micromechanical approach can be utilised. Both the governing equations for the curing simulation framework and the necessary details for the numerical implementation within the finite element method are derived. The curing of polymers is a very complex process involving a series of chemical reactions typically resulting in a conversion of low molecular weight monomer solutions into more or less cross-linked solid macromolecular structures. A material undergoing such a transition can be modelled by using an appropriate constitutive relation that is distinguished by prescribed temporal evolutions of its governing material parameters, which have to be determined experimentally. Part I of this work will deal with the elastic framework whereas the following Part II will focus on viscoelastic behaviour and shrinkage effects. Some numerical examples demonstrate the capability of our approach to correctly reproduce the behaviour of curing materials.
KeywordsCuring Polymer Finite strains Elasticity
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- 3.Kiasat M (2000) Curing shrinkage and residual stresses in viscoelastic thermosetting resins and composites. Ph.D. Thesis, TU Delft, NetherlandsGoogle Scholar
- 4.van ’t Hof C (2006) Mechanical characterization and modeling of curing thermosets. Ph.D. Thesis, TU Delft, NetherlandsGoogle Scholar
- 6.Adolf DB, Martin JE (1996) Calculation of stresses in crosslinking polymers. J Compos Mater 30: 13–34Google Scholar
- 13.Retka J, Höfer P (2007) Numerische Simulation aushärtender Klebstoffe. Diploma Thesis, Universität der Bundeswehr MünchenGoogle Scholar
- 17.Boyce MC, Arruda EM (2000) Constitutive models of rubber elasticity: a review. Rubber Chem Technol 73: 504–523Google Scholar
- 18.Marckmann G, Verron E (2006) Comparison of hyperelastic models for rubber-like materials. Rubber Chemistry Technol 79: 835–858Google Scholar
- 20.Lulei F (2002) Mikromechanisch motivierte Modelle zur Beschreibung finiter Deformationen gummiartiger Polymere: Physikalische Modellbildung und Numerische Simulation. Ph.D. Thesis, Institut für Mechanik (Bauwesen), University of StuttgartGoogle Scholar
- 21.Göktepe S (2007) Micro-macro approaches to rubbery and glassy polymers: Predictive micromechanically-based models and simulations. Ph.D. Thesis, Institüt für Mechanik (Bauwesen), University of StuttgartGoogle Scholar
- 26.Dal H, Kaliske M (2009) A micro-continuum-mechanical material model for failure of rubber-like materials: application to ageing induced fracturing. doi:10.1016/j.jmps.2009.04.007