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Formulation Derivation to Analyze the Non-linear Mechanical Behavior of Living Tissues in the Growth and Remodeling Processes Based on non- Classical Continuum Theories

Javadi Sigaroudi, Mohammad Javad | 2020

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 53347 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Sohrabpour, Saeed; Asghari, Mohsen
  7. Abstract:
  8. Research in the field of medical science goes back decades and significant progress has been made in understanding the behavior of organs and living tissues. Consequently, scientists need to work towards identifying how to mathematically model the mechanical behavior of these living organisms. If we consider any living entity, we can see that they are a product of atoms, molecules, cells, tissues, and/or organs. Differential geometry and continuum mechanics indicate that during the growth process these organisms are influenced by the phenomena of aging, remodeling and morphogenesis. The majority of research in this area, i.e. the study of these important phenomena in living tissues, has focused on using classical continuum mechanics. However, the literature shows that the theory of classical continuum mechanics comes up short in the sense that it does not provide accurate results. For example, this theory is not able to capture the effects of mass flux in the mechanical modeling of living tissues due to its kinematics limitations. Additionally, all living organisms have microstructures within themselves. While, classical continuum mechanics is unable to model the exact behavior of materials with microstructures. Therefore, in order to overcome the challenges placed by classical continuum mechanics, the theory of generalized continuum mechanics, including theories such as strain gradient, couple stress, micromorphic, and micropolar can be used. The main objective of the current thesis is to investigate the growth and remodeling processes of living tissues using the couple stress and micromorphic theories. In order to meet this objective for both theories, a number of steps have to be taken. Firstly, kinematic behavior is defined through the use of differential geometry. Secondly, balance equations with the inclusion of the effects of mass flux and mass production, are developed through the use of the principle of material frame indifference. Thirdly, appropriate constitutive equations with consideration for the material length scale are extracted. Finally, the growth and remodeling evolution laws are defined within the framework of the theory of uniformity.It should be noted that our investigations on the growth and remodeling processes via the micromorphic theory lead to new definitions of these processes in the microstructure via the variation of the microinertia. Our research output allows us to identify the fact that these processes are dependent on the evolution of the micromorphic material transplant which yields the change in density and microinertia. In order to study the effects of the evolution laws on the growth and remodeling processes for the couple stress and the micromophic theory, a numerical study is designed for each theory. The first study is based on the couple stress theory where the volumetric growth of a cubic isotrorpic chunk is investigated. This study shows that due to the effects of the couple stress tensor, we have an increase in the rate of growth. Then, based on the micromorphic theory the remodeling process of the biological tissues under the simple shear loading is studied which shows a significant decrease in the stress components
  9. Keywords:
  10. Length Scale ; Couple Stress ; Constitutive Equations ; Uniformity Coefficient ; Remodeling ; Growth ; Mass Flux ; Continuum Mechanics ; Micromorphic Theory

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