Summary of Mechanics doctoral thesis: Equivalent inclusion approximation for effective properties of compound inclusion composites

Building approximation formulas using equivalentinclusion method to determine the effective values of the conductivity, the elastic modulus of compound-inclusion composite materials and applying numerical methods using finite elements (FE) calculated for some specific material models.
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Summary of Mechanics doctoral thesis: Equivalent inclusion approximation for effective properties of compound inclusion composites MINISTRY OF EDUCATION VIETNAM ACADEMY OF AND TRAINING SCIENCE AND TECHNOLOGYGRADUATE UNIVERSITY SCIENCE AND TECHNOLOGY ----------------------------------- NGUYEN THI HUONG GIANG EQUIVALENT-INCLUSION APPROXIMATION FOR EFFECTIVE PROPERTIES OF COMPOUND-INCLUSION COMPOSITES Major: Mechanics of Solid Code: 944 01 07 SUMMARY OF MECHANICS DOCTORAL THESIS HA NOI 2020The thesis has been completed at: Graduate University Science andTechnology-Vietnam Academy of Science and Technology.Supervision: 1. Prof. Dr. of Sci. Pham Duc Chinh 2. Assoc. Prof. Dr. Tran Bao VietRiviewer 1: Prof. Dr. Hoang Xuan LuongRiviewer 2: Assoc. Prof. Dr. Nguyen Trung KienRiviewer 3: Assoc. Prof. La Duc VietThesis is defended at Graduate University Science and TechnologyVietnam Academy of Science and Technologyat................on.................Hardcopy of the thesis be found at:- Library of Graduate University Science and Technology- Vietnam national library 1 PREFACE1. Urgency of thesis In the producing composite materials, due to thechemical reaction between the matrix phase and inclusion phaseor by the coating technique of fibers to form an intermediatephase (the shell surrounding the inclusion - interface), which inthe thesis is called materials with compound inclusion.Compound inclusion is understood as the inclusion and the shellsurrounding its. This shell has mechanical - physical propertiesunlike the matrix or inclusion and affects the macroscopicproperties of the material. Then, if the upper and lower boundsmethod is used to determine the effective values, the bounds areoften far apart, with little actual value. The effective mediumapproximation methods analyzed using a cylindrical or multi-layered spherical model are relatively complex when used forcalculation engineers. Therefore, the research direction in thethesis is determination of macro mechanical - physical propertiesof compound - inclusion composite materials, using equivalentinclusion method to give simple approximation formulas. Theyare suitable for engineers to initially assess the mechanicalproperties of the materials used. Numerical simulations by finiteelement method are also applied to test the correctness of theapproximation formula.2. Objectives of the thesis Building approximation formulas using equivalent-inclusion method to determine the effective values of theconductivity, the elastic modulus of compound-inclusioncomposite materials and applying numerical methods using finiteelements (FE) calculated for some specific material models.3. Contents of the thesis Determine the effective conductivity of unidirectionalcoated-fiber composite materials, the coating shell isotropic oranisotropic (chapter 2). Determine the effective elastic modulus of compound –spherical inclusion composite and unidirectional coated-fibercomposite materials (chapter 3). 2Applying numerical method using finite element to calculate forsome periodic composite materials (chapter 4). CHAPTER 1. OVERVIEW1.1. Classification composite material1.1.1. Based on inclusions Composite has 2 types: particle reinforced and fiberreinforced.1.1.2. Based on matrices Composite has 3 types: polymer matrix, metal matrix,ceramic matrix.1.2. Conductivity Thermal conductivity c, electrical conductivity c, diffusionD, fluid permeability k, electric permittivity ϵ, magneticpermeability μ. They have the same mathematical formula andsatisfies the same equilibrium equation. Therefore, in the thesisuses thermal conductivity in calculations and illustrativeexamples to characterize the conductivity.1.3. Elastic modulus Young’s modulus E, shear modulus µ, bulk modulus k,Poisson’s ratio ν.1.4. Representative Volume Element The representative volume element (RVE) must be largeenough for the microstructures to represent the properties of thecomposite material and at the same time small enough for the sizeof the object to determine the macroscopic properties. Fig 1.3 . Representative volume element RVE 3The RVE consists of n components occupying regions V Vand having isotropic conductivities c , elastic modulus k , (α = 1,…, n).1.5. Approximations and bounds on the effective properties of composite materials1.5.1. Effective medium approximations1.5.1.1. Differential approximation n  I  ...