The Inclusion-Based Boundary Element Method (iBEM) is an innovative numerical method for the study of the multi-physical and mechanical behaviour of composite materials, linear elasticity, potential flow or Stokes fluid dynamics. It combines the basic ideas of Eshelby's Equivalent Inclusion Method (EIM) in classic micromechanics and the Boundary Element Method (BEM) in computational mechanics.
The book starts by explaining the application and extension of the EIM from elastic problems to the Stokes fluid, and potential flow problems for a multiphase material system in the infinite domain. It also shows how switching the Green's function for infinite domain solutions to semi-infinite domain solutions allows this method to solve semi-infinite domain problems. A thorough examination of particle-particle interaction and particle-boundary interaction exposes the limitation of the classic micromechanics based on Eshelby's solution for one particle embedded in the infinite domain, and demonstrates the necessity to consider the particle interactions and boundary effects for a composite containing a fairly high volume fraction of the dispersed materials.
Starting by covering the fundamentals required to understand the method and going on to describe everything needed to apply it to a variety of practical contexts, this book is the ideal guide to this innovative numerical method for students, researchers, and engineers.
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Table of Contents
Introduction: Virtual experiments with iBEM 2. Fundamental solutions: Potential flow, elastic, and Stokes flow problems 3. Integrals of Green's functions and their derivatives: Eshelby's tensor for elastic inclusion problems 4. The equivalent inclusion method: Inhomogeneity problems in an unbounded domain 5. The iBEM formulation and implementation: Ellipsoidal inhomogeneities in a bounded domain 6. The iBEM implementation with particle discretization: Polyhedral inhomogeneities 7. The iBEM for potential problems: Scalar potential flows heat conduction 8. The iBEM for the Stokes flows: Incompressible vector potential 9. The iBEM for time-dependent loads and material behavior: Dynamics, transient heat conduction, and viscoelasticity 10. The iBEM for multiphysical problems: Advanced applications 11. Recent development toward future evolution: A powerful tool for virtual experiments
Appendix A Introduction and documentation of the iBEM software package: Code structure and a case study