The Material Point Method

The Material Point Method

A Continuum-Based Particle Method for Extreme Loading Cases

1st Edition - October 21, 2016

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  • Authors: Xiong Zhang, Zhen Chen, Yan Liu
  • eBook ISBN: 9780124078550
  • Hardcover ISBN: 9780124077164

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The Material Point Method: A Continuum-Based Particle Method for Extreme Loading Cases systematically introduces the theory, code design, and application of the material point method, covering subjects such as the spatial and temporal discretization of MPM, frequently-used strength models and equations of state of materials, contact algorithms in MPM, adaptive MPM, the hybrid/coupled material point finite element method, object-oriented programming of MPM, and the application of MPM in impact, explosion, and metal forming. Recent progresses are also stated in this monograph, including improvement of efficiency, memory storage, coupling/combination with the finite element method, the contact algorithm, and their application to problems.

Key Features

  • Provides a user’s guide and several numerical examples of the MPM3D-F90 code that can be downloaded from a website
  • Presents models that describe different types of material behaviors, with a focus on extreme events.
  • Includes applications of MPM and its extensions in extreme events, such as transient crack propagation, impact/penetration, blast, fluid-structure interaction, and biomechanical responses to extreme loading


Scientific researchers, technicians, engineers and graduate students for their research and studies

Table of Contents

    • Dedication
    • About the Authors
    • Preface
      • Bibliography
    • Chapter 1: Introduction
      • Abstract
      • 1.1. Lagrangian Methods
      • 1.2. Eulerian Methods
      • 1.3. Hybrid Methods
      • 1.4. Meshfree Methods
      • Bibliography
    • Chapter 2: Governing Equations
      • Abstract
      • 2.1. Description of Motion
      • 2.2. Deformation Gradient
      • 2.3. Rate of Deformation
      • 2.4. Cauchy Stress
      • 2.5. Jaumann Stress Rate
      • 2.6. Updated Lagrangian Formulation
      • 2.7. Weak Form of the Updated Lagrangian Formulation
      • 2.8. Shock Wave
      • 2.9. Detonation Wave
      • Bibliography
    • Chapter 3: The Material Point Method
      • Abstract
      • 3.1. Material Point Discretization
      • 3.2. Explicit Material Point Method
      • 3.3. Contact Method
      • 3.4. Generalized Interpolation MPM and Other Improvements
      • 3.5. Adaptive Material Point Method
      • 3.6. Non-reflecting Boundary
      • 3.7. Incompressible Material Point Method
      • 3.8. Implicit Material Point Method
      • Bibliography
    • Chapter 4: Computer Implementation of the MPM
      • Abstract
      • 4.1. Execution of the MPM3D-F90
      • 4.2. Input Data File Format of the MPM3D-F90
      • 4.3. Source Files of the MPM3D-F90
      • 4.4. Free Format Input
      • 4.5. MPM Data Encapsulation
      • 4.6. Main Subroutines
      • 4.7. Numerical Examples
      • Bibliography
    • Chapter 5: Coupling of the MPM with FEM
      • Abstract
      • 5.1. Explicit Finite Element Method
      • 5.2. Hybrid FEM and MPM
      • 5.3. Coupled FEM and MPM
      • 5.4. Adaptive FEMP Method
      • Bibliography
    • Chapter 6: Constitutive Models
      • Abstract
      • 6.1. Stress Update
      • 6.2. Strength Models
      • 6.3. Equation of State
      • 6.4. Failure Models
      • 6.5. Computer Implementation of Material Models
      • Bibliography
    • Chapter 7: Multiscale MPM
      • Abstract
      • 7.1. Governing Equations at Different Scales
      • 7.2. Solution Scheme for Concurrent Simulations
      • 7.3. Interfacial Treatment
      • 7.4. Demonstration
      • Bibliography
    • Chapter 8: Applications of the MPM
      • Abstract
      • 8.1. Fracture Evolution
      • 8.2. Impact
      • 8.3. Explosion
      • 8.4. Fluid–Structure/Solid Interaction
      • 8.5. Multiscale Simulation
      • 8.6. Biomechanics Problems
      • 8.7. Other Problems with Extreme Deformations
      • Bibliography
    • Bibliography
    • Index

Product details

  • No. of pages: 300
  • Language: English
  • Copyright: © Academic Press 2016
  • Published: October 21, 2016
  • Imprint: Academic Press
  • eBook ISBN: 9780124078550
  • Hardcover ISBN: 9780124077164

About the Authors

Xiong Zhang

Xiong Zhang received his Ph.D. in Computational Mechanics from the Dalian University of Technology in 1992. He is now a professor in the School of Aerospace Engineering at Tsinghua University, and the Associate Editor of the International Journal of Mechanics and Materials in Design. His selected honors include the New Century Excellent Talents in University (Ministry of Education of China, 2004), the First prize (2008) and Second prize (2009) for Natural Science from the Ministry of Education of China, the ICACM Fellows Award (2011), the Beijing Municipal Famous Teacher Award for Higher Education (2015) and the Qian Lingxi Computational Mechanics Award (Achievement Award, 2016). His current research interests focus on numerical modeling of extreme events, such as hypervelocity impact, blast, bird impact, penetration, perforation and fluid-structure interaction. He has published 3 monographs and 3 textbooks in Chinese. He was included in the list of Elsevier’s “Most Cited Chinese Researchers” in 2015.

Affiliations and Expertise

Professor, School of Aerospace Engineering, Tsinghua University, China

Zhen Chen

His research area is in Computation Mechanics with a recent focus on multiscale modeling and simulation of the multiphysical phenomena involved in structural failure subjected to extreme loading conditions. Before joining MU in 1995, he was a professional staff member at New Mexico Engineering Research Institute as well as in the Department for the Waste Isolation Pilot Project/Performance Analysis Code Development at Sandia National Laboratories.

Among his honors and awards are the Fellow of ASME, the Fellow of the ICACM, the Yangtze visiting professor and Qianren-Plan visiting professor appointed by the Ministry of Education in China, the Faculty Research Award in the College of Engineering at MU, the Outstanding Youth Award (Oversea) from the National Natural Science Foundation of China, and the NSF-CAREER Award. He received his Ph.D. in solid and computational mechanics from the University of New Mexico in 1989.

Affiliations and Expertise

C.W. LaPierre Professor of Engineering, University of Missouri (MU), Columbia, MO, USA

Yan Liu

did his postdoctoral research at Northwestern University from 2008 to 2010. He has been a faculty member at Tsinghua University since 2010, and is now an

associate professor in the School of Aerospace Engineering.His research interests include multiscale simulation, meshfree particle methods and impact dynamics.

He received the Natural Science Award from Chinese Ministry of Education in 2009, Du Qing-Hua Medal & Young Researcher Award of Computational Methods in Engineering in 2012, the ICACM Young Investigator Award in 2013.

Affiliations and Expertise

Associate professor, School of Aerospace Engineering, Tsinghua University, Beijing, China

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  • George W. Fri Dec 29 2017

    Good writing with essential contents

    Clear writing book. The contents are essential in the subject and contains application algorithms. It is possible to compile the source code to verify and study the developed concepts.