The Inclusion-Based Boundary Element Method (iBEM)

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.

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

Huiming Yin is an associate professor in the Department of Civil Engineering and Engineering Mechanics at Columbia University, and the director of the NSF Center for Energy Harvesting Materials and Systems at Columbia Site. His research specializes in the multiscale/physics characterization of civil engineering materials and structures with experimental, analytical, and numerical methods. His research interests are interdisciplinary and range from structures and materials to innovative construction technologies and test methods. He has taught courses in energy harvesting, solid mechanics, and composite materials at Columbia University.
Dr. Gan Song obtained his Ph.D. in the Department of Civil Engineering and Engineering Mechanics at Columbia University. His research interest focuses on numerical simulation of the mechanical behaviour of civil engineering materials. He develops this innovative numerical method - iBEM under the advice of Professor Yin, which is a powerful tool to characterize mechanical property of composite material containing various sizes, shapes and types of particles within affordable computational cost. The method is able to be extended to analyse fluid mechanics, potential flow, and other multi-physical problems as well.
Liangliang Zhang is an Associate Research Scientist in the Department of Civil Engineering and Engineering Mechanics at Columbia University. He earned his Ph. D. in Engineering Mechanics at China Agricultural University. Before joining Columbia University in 2017, he worked as an engineer in company for two years and obtained multidisciplinary engineering experience covering innovative structural design and materials. His research interests are focus on the advanced smart materials and composite structures.
Chunlin Wu, PhD from Civil Engineering and Engineering Mechanics, specializes in the iBEM software developing. He received a BS in civil engineering from Tongji University, China in 2017, MS in engineering mechanics from Columbia University, 2018, and PhD in engineering mechanics from Columbia University in October 2021. He received the Mindlin's scholar award in Civil engineering and Engineering mechanics for his PhD studies.