Ab initio DFPT Based Constitutive Modelling of Crystalline Solids within Micromorphic Theory with Application to Nano/Micro-structures

Moosavian, Hashem | 2020

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 53595 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Mohammad Shodja, Hossein
  7. Abstract:
  8. To account for certain essential features of material such as micro-structure effects and dispersive behaviour and optical branches in dispersion curves, a fundamental departure from classical elasticity to generalized continuum theories is required. Among the generalized continuum mechanics, micromorphic elasticity is capable of capturing these physical phenomena completely. In the mathematical framework of micromorphic elasticity, in addition to the traditional elastic moduli tensors, some additional tensors are introduced in the pertinent governing equations of motion. A precise evaluation of the numerical values of the aforementioned elastic moduli tensors in the realm of the experimentations poses serious difficulties. Thus this work aims to provide a remedy as how to determine the micromorphic elastic moduli tensors theoretically in terms of the atomic force constants and lattice parameters of the crystalline solid with general anisotropy. To this end, the discrete lattice dynamics equations of a crystal are related to the pertinent anisotropic micromorphic equations of motion. This approach allows incorporating the symmetry groups of the crystals within lattice dynamics equations conveniently. For the illustration of the current theoretical developments, the closed forms of the micromorphic elastic moduli tensors are obtained in terms of elastic constants for diamond structures and these constants are computed in conjunction with ab initio density functional perturbation theory (DFPT) for diamond and silicon. The accuracy of the results is verified by comparing the dispersion curves derived from the micromorphic theory, those of available experiments, and those directly obtained from DFPT calculations. It should be mentioned that the current research deals with the micromorphic elasticity in both local and weakly nonlocal form
  9. Keywords:
  10. Micromorphic Theory ; Density Functional Theory (DFT) ; Lattice Dynamics Theory ; Elastic Moduli Tensors ; Diamond Structures ; Atomic Force Constants

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