Graduate Thesis Or Dissertation

Theory of micromorphic materials and applications

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  • A general theory of micromorphic materials was developed by Eringen for the prediction of continuum behavior of materials with inner structure, such as, granular solids, composite materials, anisotropic and polymeric fluids. Recently Eringen derived balance laws of micromorphic mechanics from a different point of view. His derivation of the master functional balance laws are reviewed and the specific forms of balance laws are obtained. In the study of viscoelastic behavior of non-Newtonian fluids it is well known that the introduction of generalized deformation-rate tensors in the constitutive equations plays an important role. In the present investigation we have introduced the concept of combined generalized measures in the micromorphic constitutive equations proposed by Eringen. In order to incorporate the viscoelastic effects, generalized measures of not only the first deformation-rate tensor involving velocity gradients, but also those of the second deformation-rate tensor involving acceleration gradients are introduced in the development of constitutive equations. The use of such generalized measures in the place of ordinary measures in constitutive equations eliminates the need for using higher order deformation-rates as shown by Narasimhan and Sra. In the present investigation we have developed a new constitutive theory for micromorphic materials by introducing in the classical constitutive equations generalized measures of deformation-rate tensors and micro-deformation-rate tensors. Using the constitutive equation based on concepts of generalized measures and basic equations of micromorphic materials of grade one, the problem of micropolar fluid flows in converging and diverging channels are investigated. The behavior of micropolar fluids is investigated in terms of a suitably defined Reynolds number and two other fluid parameters--the viscoelastic parameter and the micro-deformation parameter. For vanishing viscoelastic parameter but for non-vanishing micro-deformation parameter, exact solutions are obtained in terms of elliptic functions. In this case it is possible to identify the Reynolds number with the Reynolds number defined in terms of the maximum velocity by other workers. Classical solutions for Newtonian fluids are found to appear as a special case of our more general solutions for micropolar fluids. For non-vanishing viscoelastic parameter, exact solutions are again obtained in terms of elliptic functions and elliptic integrals. Numerical and graphical solutions are obtained to study the micropolar fluid flow between converging and diverging channels.
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