The Material Point Method

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.

• 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

• 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 Up