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Determination of Primary Function and Associated Spin Tensor For Linear Rate Type Isotropic Tensor Functions

Momeni, Alireza | 2011

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 42180 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Sohrabpour, Saeed; Asghari, Mohsen
  7. Abstract:
  8. In modelling of large deformations in deformable solids, rate type constitutive equations are of great importance. In order to fulfill the material objectivity conditions it is necessary to choose an objective rate of stress tensor. On the other hand, using corotational rates, because of their special properties (which are resulted of the fact that varaition of parameters are computed from an observer connected to a rotated triad), in rate type non-linear elastic constitutive equations (called hypo-elastic equations) are notable. In this thesis, the necessary conditions for a linear rate type isotropic tensor-valued function of a tensor argument and its rate to be integrable are driven. In other words, the necessary conditions for existence of an isotropic tensor function (called primary function) which its corotational rate is equal to the considered linear rate type function, are obtained. Also it is explained that how can the type of corotional rate be determined ( i.e., how can components of associated spin tensor be calculated), if the necessary conditions are satisfied. Each constitutive equation which is not integrable results in dependency of elastic behavior of the material to the path (history) of deformation and this is in contrast with the governing rules on elastic behavior of the material. For example, using a non-integrable hypo-elastic constitutive equation in analysis of a material undergoing a closed deformation path can result in computing residual stresses at the end of the deformation. In this thesis, by using the necessary conditions for integrability, the integrability of the hypo-elastic constitutive equations is considered.
  9. Keywords:
  10. OBJECTIVE RATES ; Corotational Rates ; Hypoelastic Model ; Spin Tensor

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