Multiscale Simulations and Mechanics of Biological Materials E-Book

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 742

Veröffentlichungsjahr: 2013

Beschreibung

Multiscale Simulations and Mechanics of Biological Materials

 A compilation of recent developments in multiscale simulation and computational biomaterials written by leading specialists in the field

Presenting the latest developments in multiscale mechanics and multiscale simulations, and offering a unique viewpoint on multiscale modelling of biological materials, this book outlines the latest developments in computational biological materials from atomistic and molecular scale simulation on DNA, proteins, and nano-particles, to meoscale soft matter modelling of cells, and to macroscale soft tissue and blood vessel, and bone simulations. Traditionally, computational biomaterials researchers come from biological chemistry and biomedical engineering, so this is probably the first edited book to present work from these talented computational mechanics researchers. 

The book has been written to honor Professor Wing Liu of Northwestern University, USA, who has made pioneering contributions in multiscale simulation and computational biomaterial in specific simulation of drag delivery at atomistic and molecular scale and computational cardiovascular fluid mechanics via immersed finite element method.

Key features:

• Offers a unique interdisciplinary approach to multiscale biomaterial modelling aimed at both accessible introductory and advanced levels
• Presents a breadth of computational approaches for modelling biological materials across multiple length scales (molecular to whole-tissue scale), including solid and fluid based approaches 
• A companion website for supplementary materials plus links to contributors’ websites (www.wiley.com/go/li/multiscale)

Leseprobe

Contents

Cover

Title Page

Copyright

About the Editors

List of Contributors

Preface

Part I: Multiscale Simulation Theory

Chapter 1: Atomistic-to-Continuum Coupling Methods for Heat Transfer in Solids

1.1 Introduction

1.2 The Coupled Temperature Field

1.3 Coupling the MD and Continuum Energy

1.4 Examples

1.5 Coupled Phonon-Electron Heat Transport

1.6 Examples: Phonon–Electron Coupling

1.7 Discussion

Acknowledgments

References

Chapter 2: Accurate Boundary Treatments for Concurrent Multiscale Simulations

2.1 Introduction

2.2 Time History Kernel Treatment

2.3 Velocity Interfacial Conditions: Matching the Differential Operator

2.4 MBCs: Matching the Dispersion Relation

2.5 Accurate Boundary Conditions: Matching the Time History Kernel Function

2.6 Two-Way Boundary Conditions

2.7 Conclusions

Acknowledgments

References

Chapter 3: A Multiscale Crystal Defect Dynamics and Its Applications

3.1 Introduction

3.2 Multiscale Crystal Defect Dynamics

3.3 How and Why the MCDD Model Works

3.4 Multiscale Finite Element Discretization

3.5 Numerical Examples

3.6 Discussion

Acknowledgments

Appendix

References

Chapter 4: Application of Many-Realization Molecular Dynamics Method to Understand the Physics of Nonequilibrium Processes in Solids

4.1 Chapter Overview and Background

4.2 Many-Realization Method

4.3 Application of the Many-Realization Method to Shock Analysis

4.4 Conclusions

Acknowledgments

References

Chapter 5: Multiscale, Multiphysics Modeling of Electromechanical Coupling in Surface-Dominated Nanostructures

5.1 Introduction

5.2 Atomistic Electromechanical Potential Energy

5.3 Bulk Electrostatic Piola–Kirchoff Stress

5.4 Surface Electrostatic Stress

5.5 One-Dimensional Numerical Examples

5.6 Conclusions and Future Research

Acknowledgments

References

Chapter 6: Towards a General Purpose Design System for Composites

6.1 Motivation

6.2 General Purpose Multiscale Formulation

6.3 Mechanistic Modeling of Fatigue via Multiple Temporal Scales

6.4 Coupling of Mechanical and Environmental Degradation Processes

6.5 Uncertainty Quantification of Nonlinear Model of Micro-Interfaces and Micro-Phases

References

Part II: Patient-Specific Fluid-Structure Interaction Modeling, Simulation and Diagnosis

Chapter 7: Patient-Specific Computational Fluid Mechanics of Cerebral Arteries with Aneurysm and Stent

7.1 Introduction

7.2 Mesh Generation

7.3 Computational Results

7.4 Concluding Remarks

Acknowledgments

References

Chapter 8: Application of Isogeometric Analysis to Simulate Local Nanoparticulate Drug Delivery in Patient-Specific Coronary Arteries

8.1 Introduction

8.2 Materials and Methods

8.3 Results

8.4 Conclusions and Future Work

Acknowledgments

References

Chapter 9: Modeling and Rapid Simulation of High-Frequency Scattering Responses of Cellular Groups

9.1 Introduction

9.2 Ray Theory: Scope of Use and General Remarks

9.3 Ray Theory

9.4 Plane Harmonic Electromagnetic Waves

9.5 Summary

References

Chapter 10: Electrohydrodynamic Assembly of Nanoparticles for Nanoengineered Biosensors

10.1 Introduction for Nanoengineered Biosensors

10.2 Electric-Field-Induced Phenomena

10.3 Geometry Dependency of Dielectrophoresis

10.4 Electric-Field-Guided Assembly of Flexible Molecules in Combination with other Mechanisms

10.5 Selective Assembly of Nanoparticles

10.6 Summary and Applications

References

Chapter 11: Advancements in the Immersed Finite-Element Method and Bio-Medical Applications

11.1 Introduction

11.2 Formulation

11.3 Bio-Medical Applications

11.4 Conclusions

References

Chapter 12: Immersed Methods for Compressible Fluid–Solid Interactions

12.1 Background and Objectives

12.2 Results and Challenges

12.3 Conclusion

References

Part III: From Cellular Structure to Tissues and Organs

Chapter 13: The Role of the Cortical Membrane in Cell Mechanics: Model and Simulation

13.1 Introduction

13.2 The Physics of the Membrane–Cortex Complex and Its Interactions

13.3 Formulation of the Membrane Mechanics and Fluid–Membrane Interaction

13.4 The Extended Finite Element and the Grid-Based Particle Methods

13.5 Examples

13.6 Conclusion

Acknowledgments

References

Chapter 14: Role of Elastin in Arterial Mechanics

14.1 Introduction

14.2 The Role of Elastin in Vascular Diseases

14.3 Mechanical Behavior of Elastin

14.4 Constitutive Modeling of Elastin

14.5 Conclusions

Acknowledgments

References

Chapter 15: Characterization of Mechanical Properties of Biological Tissue: Application to the FEM Analysis of the Urinary Bladder

15.1 Introduction

15.2 Inverse Approach for the Material Characterization of Biological Soft Tissues via a Generalized Rule of Mixtures

15.3 FEM Analysis of the Urinary Bladder

15.4 Conclusions

Acknowledgments

References

Chapter 16: Structure Design of Vascular Stents

16.1 Introduction

16.2 Ideal Vascular Stents

16.3 Design Parameters that Affect the Properties of Stents

16.4 Main Methods for Vascular Stent Design

16.5 Vascular Stent Design Method Perspective

References

Chapter 17: Applications of Meshfree Methods in Explicit Fracture and Medical Modeling

17.1 Introduction

17.2 Explicit Crack Representation

17.3 Meshfree Modeling in Medicine

Acknowledgments

References

Chapter 18: Design of Dynamic and Fatigue-Strength-Enhanced Orthopedic Implants

18.1 Introduction

18.2 Fatigue Life Analysis of Orthopedic Implants

18.3 LSP Process

18.4 LSP Modeling and Simulation

18.5 Application Example

18.6 Summary

Acknowledgments

References

Part IV: Bio-mechanics and Materials of Bones and Collagens

Chapter 19: Archetype Blending Continuum Theory and Compact Bone Mechanics

19.1 Introduction

19.2 ABC Formulation

19.3 Constitutive Modeling in ABC

19.4 The ABC Computational Model

19.5 Results and Discussion

19.6 Conclusion

Acknowledgments

References

Chapter 20: Image-Based Multiscale Modeling of Porous Bone Materials

20.1 Overview

20.2 Homogenization of Porous Microstructures

20.3 Level Set Method for Image Segmentation

20.4 Image-Based Microscopic Cell Modeling

20.5 Trabecular Bone Modeling

20.6 Conclusions

Acknowledgment

References

Chapter 21: Modeling Nonlinear Plasticity of Bone Mineral from Nanoindentation Data

21.1 Introduction

21.2 Methods

21.3 Results

21.4 Conclusions

Acknowledgments

References

Chapter 22: Mechanics of Cellular Materials and its Applications

22.1 Biological Cellular Materials

22.2 Engineered Cellular Materials

References

Chapter 23: Biomechanics of Mineralized Collagens

23.1 Introduction

23.2 Computational Method

23.3 Results

23.4 Summary and Conclusions

Acknowledgments

References

Index

This edition first published 2013 © 2013 John Wiley & Sons, Ltd

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Library of Congress Cataloging-in-Publication Data

Multiscale simulations and mechanics of biological materials / edited by Professor Shaofan Li, Dr Dong Qian. pages cm Includes bibliographical references and index. ISBN 978-1-118-35079-9 (cloth) 1. Biomechanics. 2. Biomedical materials–Mechanical properties. 3. Multiscale modeling. I. Li, Shaofan, editor of compilation. II. Qian, Dong, editor of compilation. QH513.M85 2013 612.7′6–dc23 2012040166

A catalogue record for this book is available from the British Library.

ISBN: 9781118350799

About the Editors

Dr. Shaofan Li is currently a Professor of Applied and Computational Mechanics at the University of California–Berkeley. Dr. Li graduated from the Department of Mechanical Engineering at the East China University of Science and Technology (Shanghai, China) with a Bachelor Degree of Science in 1982; he also holds Master Degrees of Science from both the Huazhong University of Science and Technology (Wuhan, China) and the University of Florida (Gainesville, FL, USA) in Applied Mechanics and Aerospace Engineering in 1989 and 1993, respectively. In 1997 Dr. Li received a PhD degree in Mechanical Engineering from the Northwestern University (Evanston, IL, USA), and he was also a post-doctoral researcher at the Northwestern University during 1997–2000. In 2000 Dr. Li joined the faculty of the Department of Civil and Environmental Engineering at the University of California–Berkeley. Dr. Shaofan Li has also been a visiting Changjiang professor in the Huazhong University of Science and Technology, Wuhan, China (2007–2010). Dr. Shaofan Li is the recipient of the A. Richard Newton Research Breakthrough Award (2008) and an NSF Career Award (2003). Dr. Li has published more than 100 articles in peer-reviewed scientific journals, and he is the author and co-author of two research monographs/graduate textbooks. ([email protected])

Dr. Dong Qian is an associate professor in the Department of Mechanical Engineering at the University of Texas at Dallas. He obtained his BS degree in Bridge Engineering in 1994 from Tongji University in China. He came to the USA in 1996 and obtained an MS degree in Civil Engineering at the University of Missouri–Columbia in 1998. He continued his study at Northwestern University from 1998 and received his PhD in Mechanical Engineering in 2002. Shortly after his graduation, he was hired as an assistant professor at the University of Cincinnati. In 2008 he was promoted to the rank of associate professor with tenure and served as the Director of Graduate Studies from 2010. In the Fall of 2012 he joined the mechanical engineering department at the University of Texas at Dallas as an associate professor (tenured). His research interests include nonlinear finite-element and meshfree methods, fatigue and failure analysis and life prediction, surface engineering, residual stress analysis, and modeling and simulation of manufacturing processes (peening, forming, etc.) and nanostructured materials with a focus on mechanical properties and multiphysics coupling mechanisms. ([email protected])

List of Contributors

Ashfaq Adnan, Mechanical and Aerospace Engineering, University of Texas at Arlington, USA ([email protected])

Facundo J. Bellomo, INIQUI (CONICET), Faculty of Engineering, National University of Salta, Argentina ([email protected])

Eduard Benet, Department of Civil, Environmental and Architectural Engineering, University of Colorado, USA ([email protected])

Sagar Bhamare, School of Dynamic Systems College of Engineering and Applied Science, University of Cincinnati, USA ([email protected])

Jiun-Shyan Chen, Department of Civil and Environmental Engineering, University of California, Los Angeles, USA ([email protected])

Sheng-Wei Chi, Department of Civil and Environmental Engineering, University of Illinos at Chicago, USA ([email protected])

Jae-Hyun Chung, University of Washington, USA ([email protected])

Suvranu De, Department of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute, New York, USA ([email protected])

Michel Devel, FEMTO-ST Institute, Université de Franche-Comté, France ([email protected])

Khalil I. Elkhodary, Department of Mechanical Engineering, Northwestern University, USA ([email protected])

Xavier Espinet, Department of Civil, Environmental and Architectural Engineering, University of Colorado, USA ([email protected])

Leonora Felon, X-spine Systems, Inc., USA ([email protected])

Sheikh F. Ferdous, Mechanical and Aerospace Engineering, University of Texas at Arlington, USA ([email protected])

Jacob Fish, Columbia University, USA ([email protected])

Louis Foucard, Department of Civil, Environmental and Architectural Engineering, University of Colorado, USA ([email protected])

Yao Fu, Department of Mechanical Engineering and Materials Science, University of Pittsburgh, USA ([email protected])

Michael Steven Greene, Theoretical & Applied Mechanics, Northwestern University, USA ([email protected])

Shaolie S. Hossain, Institute for Computational Engineering and Sciences, The University of Texas at Austin, USA ([email protected])

Jia Hu, Department of Mechanical Engineering and Mechanics, Lehigh University, USA; School of Mechanical Mechanics and Engineering, Southwest Jiaotong University, People's Republic of China ([email protected])

Daeyong Kim, Korea Institute of Materials Science, South Korea ([email protected])

Ji Hoon Kim, Korea Institute of Materials Science, South Korea ([email protected])

Jong-Hoon Kim, University of Washington, USA ([email protected])

David Kirschman, X-spine Systems, Inc., USA ([email protected])

Nikolay Kostov, Mechanical Engineering, Rice University, USA ([email protected])

Hyun-Boo Lee, University of Washington, USA ([email protected])

Myoung-Gyu Lee, Pohang University of Science and Technology, South Korea ([email protected])

Lisheng Liu, Department of Civil and Environmental Engineering, The University of California at Berkeley, USA; Department of Engineering Structure and Mechanics, Wuhan University of Technology, People's Republic of China ([email protected])

Yaling Liu, Department of Mechanical Engineering and Mechanics, Lehigh University, USA; Bio-engineering Program, Lehigh University, USA ([email protected])

Seetha Ramaiah Mannava, School of Dynamic Systems College of Engineering and Applied Science, University of Cincinnati, USA ([email protected])

Virginia Monteiro, International Center for Numerical Method in Engineering (CIMNE), Technical University of Catalonia, Spain ([email protected])

Liz G. Nallim, INIQUI (CONICET), Faculty of Engineering, National University of Salta, Argentina ([email protected])

Devin O'Connor, Department of Mechanical Engineering, Northwestern University, USA ([email protected])

Sergio Oller, International Center for Numerical Method in Engineering (CIMNE), Technical University of Catalonia, Spain ([email protected])

Eugenio Oñate, International Center for Numerical Method in Engineering (CIMNE), Technical University of Catalonia, Spain ([email protected])

Harold S. Park, Department of Mechanical Engineering, Boston University, USA ([email protected])

Anthony Puntel, Mechanical Engineering, Rice University, USA ([email protected])

Farzad Sarker, Mechanical and Aerospace Engineering, University of Texas at Arlington, USA ([email protected])

Kathleen Schjodt, Mechanical Engineering, Rice University, USA ([email protected])

Daniel C. Simkins, Jr., University of South Florida, USA ([email protected])

Kenji Takizawa, Department of Modern Mechanical Engineering and Waseda Institute for Advanced Study, Waseda University, Japan ([email protected]) or ([email protected])

Shaoqiang Tang, HEDPS, CAPT & Department of Mechanics, Peking University, People's Republic of China ([email protected])

Tayfun E. Tezduyar, Mechanical Engineering, Rice University, USA ([email protected])

Albert C. To, Department of Mechanical Engineering and Materials Science, University of Pittsburgh, USA ([email protected])

Vijay Vasudevan, School of Dynamic Systems College of Engineering and Applied Science, University of Cincinnati, USA ([email protected])

Franck J. Vernerey, Department of Civil, Environmental and Architectural Engineering, University of Colorado, USA ([email protected])

Gregory J. Wagner, Sandia National Laboratories, USA ([email protected])

Chu Wang, Department of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute, New York, USA ([email protected])

Xiaodong Sheldon Wang, College of Science and Mathematics, Midwestern State University, Texas, USA ([email protected])

Xingshi Wang, Department of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, New York, USA ([email protected])

Jie Yang, Department of Mechanical Engineering and Mechanics, Lehigh University, USA ([email protected])

Judy P. Yang, Department of Civil & Environmental Engineering, National Chiao Tung University, Taiwan ([email protected])

Amir Reza Zamiri, Department of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute, New York, USA ([email protected])

Shahrokh Zeinali-Davarani, Department of Mechanical Engineering, Boston University, USA ([email protected])

Yongjie Zhang, Department of Mechanical Engineering, Carnegie Mellon University, USA ([email protected])

Lucy Zhang, Department of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute, New York, USA ([email protected])

Yanhang Zhang, Department of Mechanical Engineering, Boston University, USA; Department of Biomedical Engineering, Boston University, USA ([email protected])

Tarek Ismail Zohdi, Department of Mechanical Engineering, University of California, Berkeley, USA ([email protected])

Yihua Zhou, Department of Mechanical Engineering and Mechanics, Lehigh University, USA ([email protected])

Preface

This book is dedicated to Professor Wing Kam Liu (or Wing Liu for those who know him well) on the occasion of his 60th birthday.

In 1976, Professor Wing Kam Liu received a BS degree in Engineering Science from the University of Illinois at Chicago with honors. It was his time at UIC where Wing Liu met Ted Belytschko, then a young assistant professor, and took his graduate course on finite-element methods. After graduation from UIC, Wing Liu was admitted as a graduate assistant at the California Institute of Technology (Caltech) under the supervision of the young Thomas J.R. Hughes, who was beginning his academic career there. During his Caltech years, Wing Liu worked on a number of research topics, including finite-element shell elements, which is known today as the Hughes–Liu element.

Wing Liu received both his MS degree (1977) and PhD degree (1980) in Civil Engineering from Caltech, and he then came back to Chicago to become an assistant professor at Northwestern University, joining Ted Belytschko and kicking off a 30-year collaboration between them. In his 32-year academic career, Professor Liu has made numerous contributions to computational mechanics and micromechanics. Among his most noteworthy contributions are:

1.Development of multiscale methods that bridge quantum to continuum mechanics. Using these methods, he has developed software for the analysis and design of nanoparticles in materials, bio-sensing, and drug delivery.

2.Development of new finite-element techniques. These include introducing new shell elements, arbitrary Eulerian–Lagrangian methods, and explicit–implicit integration techniques that have significantly enhanced the accuracy and speed in software for crashworthiness and prototype simulations. Wing Liu was also the first to develop nonlinear probabilistic finite-element techniques that made nonlinear stochastic and reliability analyses possible.

3.Development of meshfree formulations known as reproducing kernel particle methods. These methods provide exceptional accuracy for the simulation of solids undergoing extremely large deformation and have been implemented in many commercial and laboratory software systems:

i shell elements in DYNA3D, ABAQUS, LS-DYNA, ANSYS, and Argonne National Laboratory (ANL) software;

ii explicit–implicit methods in US Ballistic Laboratory EPIC-2/EPIC-3 programs, and ANL software;

iii Lagrangian–Eulerian methods adopted by ANL, Kawasaki, Mitsubishi, Ford Motors, and Grumman;

iv various meshfree methods implemented by Sandia National Labs, Lawrence Livermore National Lab, General Motors, Ford Motors, Delphi, Ball Aerospace, and Caterpillar;

v multiscale methods adopted by Goodyear for the design of tires and by Sandia in their TAHOE code for multiscale analysis.

Professor Wing Kam Liu is the recipient of numerous awards and honors that include: the 2012 Gauss–Newton Medal (IACM Congress Medal), the highest award given by IACM; the 2009 ASME Dedicated Service Award; the 2007 ASME Robert Henry Thurston Lecture Award; the 2007 USACM John von Neumann Medal, the highest honor given by USACM; the 2004 Japan Society of Mechanical Engineers (JSME) Computational Mechanics Award; the 2002 IACM Computational Mechanics Award; the 2001 USACM Computational Structural Mechanics Award; the 1995 ASME Gustus L. Larson Memorial Award; the 1985 ASME Pi Tau Sigma Gold Medal; the 1979 ASME Melville Medal (for best paper); the 1989 Thomas J. Jaeger Prize of the International Association for Structural Mechanics; and the 1983 Ralph R. Teetor Educational Award, American Society of Automotive Engineers. In 2001, he is listed by ISI as one of the most highly cited and influential researchers in engineering.

This large number of accolades highlights Wing Liu as a scholar and educator of extraordinary international reputation. This is also underlined by the fact that the present book comprises contributions from North American, Europe, and Asia, and from a very diverse group of people: colleagues, friends, collaborators, and former and current PhD students and post-docs. A wide range of topics is covered in this book: multiscale methods, atomistic simulations, micromechanics, and biomechanics/biophysics. These contributions represent either Wing Kam Liu's own research activities or topics he has taken an interest in over recent years. Moreover, the dedications of the contributing authors show that Wing Liu has represented more than just a scientist to a great number of people, to whom he also serves as friend, supporter, and source of inspiration. We are glad to have the opportunity of editing this book and would like to thank Wiley for its helpful collaboration, the authors for their contributions and making this book a success, and Wing Liu for his inspiring and initiating novel research in computational mechanics.

On behalf of the authors, we congratulate Wing Kam Liu to his 60th birthday and wish him happiness, health, success, and continued intellectual creativity for the years to come.

Shaofan Li and Dong Qian Houston, TexasNovember 2012

Part I

Multiscale Simulation Theory

Atomistic and multiscale simulation research is one of the current focuses of computational mechanics. In Part One we present a group of recent research studies in this active research area. Some of the chapters presented in this book contain research topics that are reported or released for the first time in the literature, and they touch almost every aspect of multiscale simulation research. In Chapter 1, Wagner presents an atomistic-based multiscale method to simulate heat transfer and energy conversion, which is a recent development of the bridging-scale method. In Chapter 2, Tang presents a detailed account on how to provide an accurate boundary treatment for concurrent multiscale simulation including the bridging-scale method. In Chapter 3, Liu and Li present for the first time a novel multiscale method called multiscale crystal-defect dynamics (MCDD), which is intended for simulation of dislocation motion, nanoscale plasticity, and small-scale fractures. In Chapter 4, Fu and To discuss their ingenious construction of a novel nonequilibrium molecular dynamics, and then Park and Devel, in Chapter 5, apply a coarse-grained multiscale method to study electromechanical coupling in surface-dominated nanostructures. In this part, Wagner, Tang, and Park were the main members of Wing Liu's research group in the early 2000s and have worked with Wing Liu in developing the bridging-scale method. The last chapter of this part is contributed by Dr. Fish, who presents a multiscale design theory and design procedure for general composite materials based on a multiscale asymptotic homogenization theory.

1

Atomistic-to-Continuum Coupling Methods for Heat Transfer in Solids

Gregory J. Wagner

Sandia National Laboratories, USA

1.1 Introduction

New scientific and technical knowledge and advances in fabrication techniques have led to a revolution in the development of nanoscale devices and nanostructured materials. At the same time, improved computational resources and tools have allowed a continuously increased role for computational simulation in the engineering design process, for products at all scales. For many nano-mechanical or nano-electronic devices, models are sought that can accurately predict thermal and thermo-mechanical behavior under the range of conditions to which the devices will be subjected. However, at these small scales the limitations of continuum thermo-mechanical modeling techniques become apparent, as the effects of surfaces, grain boundaries, defects, and other deviations from a perfect continuum become important. Fourier’s law, (where q is heat flux density, κ is the thermal conductivity, and is the local temperature gradient) may not be applicable, nor may macroscale stress and strain laws; in fact, concepts like stress, strain, and even temperature may be difficult to define at the atomic scale.

Atomistic simulation techniques like molecular dynamics (MD) provide a way to simulate these small-scale behaviors, especially when combined with an accurate and efficient interatomic potential or force law that allows simulations of billions of atoms. However, even the very largest MD simulations may not be able to capture large enough length scales to simulate the interscale interactions important in real devices (since, typically, a nanoscale device must at some level be addressable from the macroscale in order to provide useful function). Classical MD has other shortcomings, as well, especially for real geometries at finite temperatures. For example, a number of approaches are available for holding an MD simulation at fixed, constant temperature [1,2]; however, it is more difficult to regulate a spatially varying temperature, except through the use of discontinuous “blocks” of atoms held at different temperatures.

Limitations of MD have led to the development of atomistic-to-continuum coupling methods [3,4], in which a continuum description (usually a finite-element discretization) of the material is used where valid, but a discrete atomistic representation of the material is used in regions where the continuum assumptions break down. Such a breakdown may occur near defects like cracks or dislocations, or in domains where the feature size is not much larger than the interatomic spacing. The atomistic and continuum descriptions are coupled together at an interface or overlap region, usually by combining the Hamiltonians of the two systems [5] or by ensuring that internal forces are properly balanced [6]. The resulting system couples the momentum equations (or, for statics, the force equilibria) of the two regions. Formation of a seamless coupling is nontrivial even for the static case (see Miller and Tadmoor [7] for an excellent review). For the dynamic case, an additional difficulty is the wave impedance mismatch at the MD–continuum boundary, leading to internal reflection of fine-scale waves back into the MD domain. Several approaches have been studied for removing these unwanted wave reflections, usually through some form of dissipation; typically, the goal in these situations is to completely remove the outgoing energy and minimize the reflected energy, optimally to zero [8–10].