Introduction to the Micromechanics of Composite Materials

Presents Concepts That Can Be Used in Design, Processing, Testing, and Control of Composite Materials Introduction to the Micromechanics of Composite Materials weaves together the basic concepts, mathematical fundamentals, and formulations of micromechanics into a systemic approach for understanding and modeling the effective material behavior of composite materials. As various emerging composite materials have been increasingly used in civil, mechanical, biomedical, and materials engineering, this textbook provides students with a fundamental understanding of the mechanical behavior of composite materials and prepares them for further research and development work with new composite materials. Students will understand from reading this book: The basic concepts of micromechanics such as RVE, eigenstrain, inclusions, and in homogeneities How to master the constitutive law of general composite material How to use the tensorial indicial notation to formulate the Eshelby problem Common homogenization methods The content is organized in accordance with a rigorous course. It covers micromechanics theory, the microstructure of materials, homogenization, and constitutive models of different types of composite materials, and it enables students to interpret and predict the effective mechanical properties of existing and emerging composites through microstructure-based modeling and design. As a prerequisite, students should already understand the concepts of boundary value problems in solid mechanics. Introduction to the Micromechanics of Composite Materials is suitable for senior undergraduate and graduate students.

IntroductionComposite MaterialsHistory of MicromechanicsA Big Picture of Micromechanics-Based ModelingBasic Concepts of MicromechanicsCase Study: Holes Sparsely Distributed in a PlateExerciseVectors and TensorsCartesian Vectors and TensorsOperations of Vectors and TensorsCalculus of Vector and Tensor FieldsPotential Theory and Helmholtz’s Decomposition TheoremGreen’s Identities and Green’s FunctionsElastic EquationsGeneral Solution and the Elastic Green’s FunctionExerciseSpherical Inclusion and InhomogeneitySpherical Inclusion ProblemIntroduction to the Equivalent Inclusion MethodSpherical Inhomogeneity ProblemIntegrals of F, ?, Fp, ?p and Their Derivatives in 3D DomainExerciseEllipsoidal Inclusion and InhomogeneityGeneral Elastic Solution Caused By an Eigenstrain through Fourier IntegralEllipsoidal Inclusion ProblemsEquivalent Inclusion Method for Ellipsoidal InhomogeneitiesExerciseVolume Integrals and Averages in Inclusion and Inhomogeneity ProblemsVolume Averages of Stress and StrainVolume Averages in Potential ProblemsStrain Energy in Inclusion and Inhomogeneity ProblemsExerciseHomogenization for Effective Elasticity Based on the Energy MethodsHill’s TheoremHill’s BoundsClassical Variational PrinciplesHashin–Shtrikman’s Variational PrincipleHashin–Shtrikman’s BoundsExerciseHomogenization for Effective Elasticity Based on the Vectorial MethodsEffective Material Behavior and Material PhasesMicromechanics-Based Models for Two-Phase CompositesExerciseHomogenization for Effective Elasticity Based on the Perturbation MethodIntroductionOne-Dimensional Asymptotic HomogenizationHomogenization of a Periodic CompositeExerciseDefects in Materials: Void, Microcrack, Dislocation, and DamageVoidsMicrocracksDislocationDamageExerciseBoundary Effects on Particulate CompositesFundamental Solution for Semi-Infinite DomainsEquivalent Inclusion Method for One Particle in a Semi-Infinite DomainElastic Solution for Multiple Particles in a Semi-Infinite DomainBoundary Effects on Effective Elasticity of a Periodic CompositeInclusion Based Boundary Element Method for Virtual Experiments of a Composite SampleExerciseReferences

Huiming Yin is an associate professor in the Department of Civil Engineering and Engineering Mechanics at Columbia University, USA Yingtao Zhao is an associate professor in the School of Aerospace Engineering at Beijing Institute of Technology, China