The material point method : a continuum-based particle method for extreme loading cases

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 equati...

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Main Authors Zhang, Xiong, Chen, Zhen, Liu, Yan
Format eBook Book
LanguageEnglish
Published Beijing Academic Press is an imprint of Elsebier 2017
Amsterdam ; Tokyo Tsinghua University Press
Elsevier Science & Technology
Academic Press
Edition1
Subjects
Finite element method
Material point method
Materials
Online AccessGet full text
ISBN9780124077164
0124077161

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Abstract 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.
AbstractList 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.
This work systematically introduces the theory, code design, and application of the material point method, covering subjects such as the spatial and temporal discretisation 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, including improvement of efficiency, memory storage, coupling/combination with the finite element method, the contact algorithm, and their application to problems.
Author Liu, Yan
Chen, Zhen
Zhang, Xiong
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ISBN 9780124077164
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Notes Includes bibliographical references (p. 265-276) and index
OCLC 961444189
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Publisher Academic Press is an imprint of Elsebier
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Snippet The Material Point Method: A Continuum-Based Particle Method for Extreme Loading Cases systematically introduces the theory, code design, and application of...
This work systematically introduces the theory, code design, and application of the material point method, covering subjects such as the spatial and temporal...
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SubjectTerms Finite element method
Material point method
Materials
TableOfContents 6.3 Equation of State -- 6.3.1 Polytropic Process -- 6.3.2 Nearly Incompressible Fluid -- 6.3.3 Linear Polynomial -- 6.3.4 JWL -- 6.3.5 Mie-Grüneisen -- 6.4 Failure Models -- 6.4.1 Effective Plastic Strain Failure Model -- 6.4.2 Hydrostatic Tensile Failure Model -- 6.4.3 Maximum Principal/Shear Stress Failure Model -- 6.4.4 Maximum Principal/Shear Strain Failure Model -- 6.4.5 Effective Strain Failure Model -- 6.5 Computer Implementation of Material Models -- 6.5.1 Module MaterialData -- 6.5.2 Module MaterialModel -- 7 Multiscale MPM -- 7.1 Governing Equations at Different Scales -- 7.2 Solution Scheme for Concurrent Simulations -- 7.2.1 Preprocessor -- 7.2.2 Central Processing Unit -- 7.3 Interfacial Treatment -- 7.4 Demonstration -- 8 Applications of the MPM -- 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 -- Index -- Back Cover
Front Cover -- The Material Point Method -- Copyright -- Dedication -- Contents -- About the Authors -- Preface -- 1 Introduction -- 1.1 Lagrangian Methods -- 1.2 Eulerian Methods -- 1.3 Hybrid Methods -- 1.3.1 Arbitrary Eulerian-Lagrangian Method and Its Variations -- 1.3.2 Particle-In-Cell Method and Its Variations -- 1.3.3 Material Point Method -- 1.4 Meshfree Methods -- 2 Governing Equations -- 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 -- 2.6.1 Reynolds' Transport Theorem -- 2.6.2 Conservation of Mass -- 2.6.3 Conservation of Linear Momentum -- 2.6.4 Conservation of Energy -- 2.6.5 Governing Equations -- 2.7 Weak Form of the Updated Lagrangian Formulation -- 2.8 Shock Wave -- 2.8.1 Rankine-Hugoniot Equations -- 2.8.2 Arti cial Bulk Viscosity -- 2.9 Detonation Wave -- 2.9.1 CJ Detonation Model -- 2.9.2 ZND Detonation Model -- 3 The Material Point Method -- 3.1 Material Point Discretization -- 3.1.1 Lagrangian Phase -- 3.1.2 Convective Phase -- 3.2 Explicit Material Point Method -- 3.2.1 Explicit Time Integration -- 3.2.2 Explicit MPM Scheme -- 3.2.3 Qualitative Demonstration -- 3.2.4 Comparison Between MPM and FEM -- 3.3 Contact Method -- 3.3.1 Boundary Conditions at Contact Surface -- 3.3.2 Contact Detection -- 3.3.3 Contact Force -- 3.3.4 Numerical Algorithm for Contact Method -- 3.4 Generalized Interpolation MPM and Other Improvements -- 3.4.1 Contiguous Particle GIMP -- 3.4.2 Uniform GIMP -- 3.4.3 Convected Particle Domain Interpolation -- 3.4.4 Dual Domain Material Point Method -- 3.4.5 Spline Grid Shape Function -- 3.5 Adaptive Material Point Method -- 3.5.1 Particle Adaptive Split -- 3.5.2 Adaptive Computational Grid -- 3.6 Non-re ecting Boundary -- 3.7 Incompressible Material Point Method
3.7.1 Momentum Equation of Fluid -- 3.7.2 Operator Splitting -- 3.7.3 Pressure Poisson Equations -- 3.7.4 Pressure Boundary Conditions -- 3.7.5 Velocity Update -- 3.8 Implicit Material Point Method -- 3.8.1 Implicit Time Integration -- 3.8.2 Solution of a System of Nonlinear Equations -- 3.8.3 The Jacobian of Grid Nodal Internal Force -- 3.8.4 Solution of a Linearized System of Equations -- 4 Computer Implementation of the MPM -- 4.1 Execution of the MPM3D-F90 -- 4.2 Input Data File Format of the MPM3D-F90 -- 4.2.1 Unit -- 4.2.2 Keywords -- 4.2.3 Global Information -- 4.2.4 Material Model -- 4.2.5 Background Grid -- 4.2.6 Solution Scheme -- 4.2.7 Results Output -- 4.2.8 Bodies -- 4.2.9 Load -- 4.2.10 An Example of Input Data File -- 4.3 Source Files of the MPM3D-F90 -- 4.4 Free Format Input -- 4.5 MPM Data Encapsulation -- 4.5.1 Particle Data -- 4.5.2 Grid Data -- 4.5.3 Data Input -- 4.5.4 Data Output -- 4.6 Main Subroutines -- 4.7 Numerical Examples -- 4.7.1 TNT Slab Detonation -- 4.7.2 Taylor Bar Impact -- 4.7.3 Perforation of a Thick Plate -- 4.7.4 Failure of Soil Slope -- 5 Coupling of the MPM with FEM -- 5.1 Explicit Finite Element Method -- 5.1.1 Finite Element Discretization -- 5.1.2 The FEM Formulation in Matrix Form -- 5.1.3 Hexahedron Element -- 5.1.4 Numerical Algorithm for an Explicit FEM -- 5.2 Hybrid FEM and MPM -- 5.3 Coupled FEM and MPM -- 5.3.1 Global Search -- 5.3.2 Local Search -- 5.3.3 Contact Force -- 5.4 Adaptive FEMP Method -- 5.4.1 Discretization Scheme -- 5.4.2 Conversion Algorithm -- 5.4.3 Coupling Between Remaining Elements and Particles -- 6 Constitutive Models -- 6.1 Stress Update -- 6.2 Strength Models -- 6.2.1 Elastic Model -- 6.2.2 Elastoplastic Models -- 6.2.3 Return Mapping Algorithm -- 6.2.4 J2 Flow Theory -- 6.2.5 Pressure-Dependent Elastoplasticity -- 6.2.6 Newtonian Fluid -- 6.2.7 High Explosive
Title The material point method : a continuum-based particle method for extreme loading cases
URI https://cir.nii.ac.jp/crid/1130576027069454099
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