COVID-19 Update: We are currently shipping orders daily. However, due to transit disruptions in some geographies, deliveries may be delayed. To provide all customers with timely access to content, we are offering 50% off Science and Technology Print & eBook bundle options. Terms & conditions.
The Material Point Method - 1st Edition - ISBN: 9780124077164, 9780124078550

The Material Point Method

1st Edition

A Continuum-Based Particle Method for Extreme Loading Cases

Authors: Xiong Zhang Zhen Chen Yan Liu
Hardcover ISBN: 9780124077164
eBook ISBN: 9780124078550
Imprint: Academic Press
Published Date: 21st October 2016
Page Count: 300
Sales tax will be calculated at check-out Price includes VAT/GST
Price includes VAT/GST

Institutional Subscription

Secure Checkout

Personal information is secured with SSL technology.

Free Shipping

Free global shipping
No minimum order.


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


No. of pages:
© Academic Press 2017
21st October 2016
Academic Press
Hardcover ISBN:
eBook ISBN:

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

Ratings and Reviews