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Constitutive Modeling of Temperature and Strain Rate Dependent Behavior of Rubbers at Finite Deformations with Combined Physicalphenomenological Approach

Khajehsaeid, Hesam | 2104

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 45412 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Naghdabadi, Reza; Sohrabpour, Saeed; Arghavani, Jamal
  7. Abstract:
  8. Wide applications of elastomeric (rubber-like) materials have led to significant interest of researchers to these materials. Elastomers as a great category of polymeric materials,posses specific properties such as large elastic deformations and energy absorption which make them suitable for aerospace and automotive applications as well as shock and vibration absorbers.In this thesis, an exponential strain energy function (SEF) has been proposed for elastomers which well reproduces the mechanical behavior of these materials and also the material parameters are related to the physical parameters of the material molecular network. This SEF has been concluded from a relation proposed for the entropy of the rubber molecular chains which is efficient even in large deformations. Considering the similar microstructure of rubbers, rubbery foams and thermoplastic elastomers, a logarithmic term has been added to the proposed SEF to extend its applicability range; thus the Exp-Ln SEF has been introduced. In order to model the Mullins effect, Marckmann’s theory has been combined with the Exp-Ln model to determine the evolution of the material parameters during deformation. By exact determination of the physical parameters of the material molecular network, it has been shown that, there is no need to constancy or reduction of the number of active monomers during deformation while emphasizing on the concepts of “active chains” and “constrained rubber”, increase of active monomers is also possible. Introducing a generalized form of separability assumption (separability of deformation and time effects), an integral nonlinear viscohyperelastic constitutive model has been proposed. Considering the physics of time dependent mechanisms and also realizing existence of secondary chain regions, the Exp-Ln SEF has been utilized for the functional of the iscous part. Therefore, the viscous stress has been obtained based on the history of the stored strain energy in the material. A rate dependent relaxation time scheme has been introduced which is consistent with physics of the time dependent mechanisms and also reduces the number of required material parameters. Furthermore, a differential method has been utilized to investigate the variation of material viscosity with respect to strain and strain rate. The proposed viscohyperalstic model has been validated in high strain rates using the data acquired from split Hopkinson pressure bar tests. Effect of temperature on the mechanical behavior of elastomers has been studied by investigating filler-filler bonds as well as filler-polymer bonds. This investigation shows nonlinear effect of temperature on the efficient volume fraction of filler particles and evolution of the properties of the molecular network. In a simple problem, it has been shown that, the linear relation between temperature and material mechanical parameters may lead to %40 errors in simulation results. To solve 3D problems, numerical formulation of the proposed model has been derived and implemented into ABAQUS via VUMAT as a new material model.Therefore, several problems concerning the applications of elastomers have been simulated and good correlations have been observed between the finite element results and those of experiments. It has been shown that, the proposed constitutive model besides its numerical formulation is a suitable and efficient tool for design and optimization of elastomeric structures and parts
  9. Keywords:
  10. Constitutive Modeling ; Elastomers ; Strain Rate ; Temperature Effect ; Finite Element Analysis ; Large Deformation ; Numerical Formulation

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