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Deriving Energy Pair Tensors for Material Strain Measures in Micropolar Continuum

Nikfar, Mohsen | 2012

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 43206 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Asghari, Mohsen
  7. Abstract:
  8. The micropolar theory is a nonclassical continuum theory which considers a microstructure associated to each particle. This microstructure has three degrees of freedom and can rigidly rotate in the three dimensional space. Beside the classical or force stress tensor, in the micropolar theory the couple stress tensor is also considered.This research is devoted to deriving energy pair tensors for material strain measures in micropolar continuum. The subject of strains and their conjugate stresses is one of the major topics in the field of solid mechanics which has greatly been dealt with in the literature. This concept was introduced for investigating structural inequalities in solid mechanics, and also has been used in nonlinear continuum mechanics and nonlinear finite element analysis.Nowadays with extending the use of small structures, the increasing needs for considering the length scale parameters in the theories are sensible. Nonclassical theories with considering the internal length scale parameter of materials and structures try to remove the limitations of classical continuum mechanics in treating small-scale structures. The purpose of this project is deriving energy pairs for Lagrangian strains in the micropolar theory. In order to derive conjugate stress tensor, the desired tensor is decomposed into two parts. One part is a rotational tensor function which is the same as the rotational part of the micropolar strains and the other part is formed by summation of a symmetric and skew symmetric tensors. Then, these parts are determined
  9. Keywords:
  10. Conjugate Stresses ; Lagrangian Strain ; Structure Equation ; Micropolar Continuum Theory

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