Summary of doctoral thesis in Mechanical engineering and Engineering mechanics: An approach to approximate and fem-model the conductivity and elasticity of multicomponent material

Equivalent inclusion approach is then developed to account for possible diversions, such as non-idealistic geometric forms of the inhomogeneities, imperfect matrix-inclusion contacts, filler dispersions, and when the particular values of the fillers’ properties are unspecified, using available numerical or experimental reference conductivity data for particular composites.
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Summary of doctoral thesis in Mechanical engineering and Engineering mechanics: An approach to approximate and fem-model the conductivity and elasticity of multicomponent material 1 MINISTRY OF EDUCATION AND VIETNAM ACADEMY OF TRAINING SCIENCE AND TECHNOLOGY GRADUATE UNIVERSITY SCIENCE AND TECHNOLOGY ----------------------------- DO QUOC HOANG AN APPROACH TO APPROXIMATE AND FEM-MODEL THE CONDUCTIVITY AND ELASTICITY OF MULTI- COMPONENT MATERIAL Major: Engineering mechanics Code: 9 52 01 01 SUMMARY OF DOCTORAL THESIS IN MECHANICAL ENGINEERING AND ENGINEERING MECHANICS Hanoi – 2019 2 The thesis has been completed at: Graduate University Science and Technology – Vietnam Academy of Science and Technology. Supervisors: 1. Assoc. Prof. DrSc. Pham Duc Chinh 2. Assoc. Prof. Dr. Tran Anh Binh Reviewer 1: Reviewer 2: Reviewer 3: Thesis is defended at Graduate University Science and Technology-Vietnam Academy of Science and Technology at ….., on ……….. Hardcopy of the thesis be found at : - Library of Graduate University Science and Technology - Vietnam national library 3 INTRODUCTION 1. Relevance of the thesis topic Most effective medium approximations for isotropic inhomogeneous materials are based on dilute solutions of some typical inclusions in an infinite matrix medium, while the simplest approximations are those for the composites with spherical and circular inclusions. Practical particulate composites often involve inhomogeneities of more complicated geometry than that of the spherical (or circular) one. In our approach, those inhomogeneities are supposed to be substituted by simple equivalent spherical (circular) inclusions from a comparison of their respective dilute solution results. Then the available simple approximations for the equivalent spherical (circular) inclusion material can be used to estimate the effective conductivity of the original composite. Numerical illustrations of the approach are performed on some 2D and 3D geometries involving elliptical and ellipsoidal inclusions. 2. Thesis objective Develop near interaction approximations for the conductivity and elasticity of multi-component materials with spherical (circular) form inclusions. Equivalent inclusion approach is then developed to account for possible diversions, such as non-idealistic geometric forms of the inhomogeneities, imperfect matrix-inclusion contacts, filler dispersions, and when the particular values of the fillers’ properties are unspecified, using available numerical or experimental reference conductivity data for particular composites. We use the eXtended Finite Elements Method (XFEM) to estimate the effective conductivity of 2D macroscopically-isotropic composites containing elliptic inclusions and the equivalent ones with circular inclusions for comparisons with the approximations. 3. Scope The thesis focuses on conductivity and elasticity of multi- component materials, the Finite Element Method (FEM) and approximation schems 4 4. Research methods  Near interaction approximations has been constructed from the minimum energy for the macroscopic conductivity and elasticity of the multi-component matrix composites with spherical (circular) inclusions. Equivalent replacement of complex-geometry inclusions by the equivalent spherical, circular, disk and needle ones with equivalent properties using polarization approximation, dilute solutions, and experimental referemce results.  Numerical method: use Matlab program to homogenize some periodic material models in the framework of FEM method (XFEM). The results of FEM are considered as the accurate reference results for comparisons with the approximation ones. 5. The contributions of the thesis Beside Introduction section, the thesis contains 3 Chapters, a Conclusion section and a list of publications relevant to the thesis. References cited in the thesis are listed at the end of the thesis. CHAPTER 1. OVERVIEW 1.1. Opening Multi-component materials have complex structures, different individual mechanical properties. Many authors offered different evaluation methods, including the effective medium approximations and the variational ones. Geometric parameters have bên added to improve the étimates. In this chapter, the author presents the concept of hômgenization and an overview of the constructions of approximation methods for complex multi-component materials. The stress field  (x) is related to the strain field  ( x) by Hook’s law:  (x)  C(x) :  (x), (1.1) The average values of the stress and strain on V is defined as: 1 1    dx ,    dx. V V V V (1.2) 5 Assume homogeneous boundary conditions for displacements: u(x)   0  x. (1.3) Or the respective ones for the tractions  n   0 n (1.4) With the solutions σ, ε on V, the relationship between the averaged stress and strain on V is presented through the effective elastic tensor Ceff:   Ceff :  , Ceff  T(k eff ,  ef ...