Numerical modelling of rubber hyperelasticity, parameter identification and finite element implementations

  • Stephen Connolly

Student thesis: Doctoral Thesis


The aim of the presented research is to investigate and develop methods to model rubber hyperelasticity. Accurate numerical modelling of the hyperelastic behaviour of rubber requires a capable constitutive model and experimental data from the material or component of interest. This research focuses on three areas: hyperelastic constitutive modelling with homogeneous experimental parameter identification, implementing hyperelasticity in the Finite Element Method and simulating the hyperelastic behaviour of industrial rubber components.;Postulated conditions are proposed to ensure the physical plausibility of hyperelastic homogeneous experimental data. Using experimental data from literature deemed to meet these conditions, the connection between constitutive model, the extent of experimental data and the ability to predict the complete hyperelastic behaviour is investigated. A more efficient means of experimental parameter identification is suggested, which uses only 'sufficient' experimental data. This data encompasses the expected range of deformations for a material or component. To develop this method for industrial rubber components, the Finite Element Method is used.;Open-source user subroutines are developed to enable the implementation of hyperelastic constitutive models in the Finite Element Method. Analytical implementations are developed for hyperelastic constitutive models defined by two common strain measures, Cauchy-Green invariants and principal stretches. Implementations are also developed for two complimentary real-domain approximation methods. All implementations are validated in terms of their numerical accuracy and computation time. The implementations are accurate to double precision and analytical methods are more computationally efficient than approximation methods.;A methodology for simulating rubber components using sufficient experimental data is developed. The approach uses prototype simulations to identify the strain region of the component under operating conditions. A modification is proposed for simulating strain-loaded and stress-loaded components, as the latter affects the strain region. The method is demonstrated by simulating two industrial components, one for each loading type.
Date of Award22 Jun 2020
Original languageEnglish
Awarding Institution
  • University Of Strathclyde
SponsorsEPSRC (Engineering and Physical Sciences Research Council)
SupervisorDonald MacKenzie (Supervisor) & Yevgen Gorash (Supervisor)

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