A Multiobjective optimization toolbox development for parameter identification of elastomers

Tekin, Tanyel
Rubber materials are widely used in industry because of their hyperelastic behaviors. Rubber materials show a highly nonlinear behavior due to hyperelastic deformability. Thus, small strain theory can not be applied to rubber materials. Various hyperelastic models are proposed by different researchers by deriving stress-stretch relations. Those relations differ in various test conditions including uniaxial, equibiaxial, pure shear and biaxial deformation modes. In this thesis, ten hyperelastic models including phenomenological and micro-mechanical models are examined. Stress definitions are obtained. Then, their efficiencies are compared by using related experimental data sets. Finally, a multiobjective optimization toolbox is developed in MATLAB GUI. Treloar data are used for parameter identification of rubber models in uniaxial, equibiaxial and pure shear cases after stress definitions are obtained for related model. Deformation gradient, right and left Cauchy-Green tensor and Kirchhoff stress differ according to each case. The Kirchhoff stresses are also decomposed into volumetric and isochoric parts. The other stresses are used in continuum mechanics are the first and second Piola-Kirchhoff stresses and Cauchy stress. The data which are used for validation of biaxial case are Kawabata data in this study. In biaxial case, the material is stretched from two orthogonal directions with different ratios. This leads to different stretches in two orthogonal directions. If those stretches are same, the case becomes equibiaxial case. In biaxial case, same tensors are obtained like other cases. In Kawabata data, there are data for stress-stretch in two directions. In present research, stress data of one of these directions are used for parameter identification procedure.


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Citation Formats
T. Tekin, “A Multiobjective optimization toolbox development for parameter identification of elastomers,” M.S. - Master of Science, Middle East Technical University, 2018.