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The Material Point Method for Geotechnical Engineering

The Material Point Method for Geotechnical Engineering Book
Author : James Fern,Alexander Rohe,Kenichi Soga,Eduardo Alonso
Publisher : CRC Press
Release : 2019-01-30
ISBN : 0429650663
Language : En, Es, Fr & De

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Book Description :

This practical guide provides the best introduction to large deformation material point method (MPM) simulations for geotechnical engineering. It provides the basic theory, discusses the different numerical features used in large deformation simulations, and presents a number of applications -- providing references, examples and guidance when using MPM for practical applications. MPM covers problems in static and dynamic situations within a common framework. It also opens new frontiers in geotechnical modelling and numerical analysis. It represents a powerful tool for exploring large deformation behaviours of soils, structures and fluids, and their interactions, such as internal and external erosion, and post-liquefaction analysis; for instance the post-failure liquid-like behaviours of landslides, penetration problems such as CPT and pile installation, and scouring problems related to underwater pipelines. In the recent years, MPM has developed enough for its practical use in industry, apart from the increasing interest in the academic world.

The Material Point Method

The Material Point Method Book
Author : Xiong Zhang,Zhen Chen,Yan Liu
Publisher : Academic Press
Release : 2016-10-26
ISBN : 0124078559
Language : En, Es, Fr & De

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Book Description :

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

Material Point Method

Material Point Method Book
Author : Jesse Russell,Ronald Cohn
Publisher : Book on Demand Limited
Release : 2012-03
ISBN : 9785511012391
Language : En, Es, Fr & De

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Book Description :

High Quality Content by WIKIPEDIA articles! The Material Point Method (MPM), is an extension of the Particle-in-cell (PIC) Method in computational fluid dynamics to computational solid dynamics, and is a Finite element method (FEM)-based particle method. It is primarily used for multiphase simulations, because of the ease of detecting contact without inter-penetration. It can also be used as an alternative to dynamic FEM methods to simulate large material deformations, because there is no re-meshing required by the MPM.

The Material Point Method for Solid and Fluid Simulation

The Material Point Method for Solid and Fluid Simulation Book
Author : Qi Guo
Publisher : Unknown
Release : 2020
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

The Material Point Method (MPM) has shown its high potential for physics-based simulation in the area of computer graphics. In this dissertation, we introduce a couple of improvements to the traditional MPM for different applications and demonstrate the advantages of our methods over the previous methods. First, we present a generalized transfer scheme for the hybrid Eulerian/Lagrangian method: the Polynomial Particle-In-Cell Method (PolyPIC). PolyPIC improves kinetic energy conservation during transfers, which leads to better vorticity resolution in fluid simulations and less numerical damping in elastoplasticity simulations. Our transfers are designed to select particle-wise polynomial approximations to the grid velocity that are optimal in the local mass-weighted L2 norm. Indeed our notion of transfers reproduces the original Particle-In-Cell Method (PIC) and recent Affine Particle-In-Cell Method (APIC). Furthermore, we derive a polynomial basis that is mass orthogonal to facilitate the rapid solution of the optimality condition. Our method applies to both of the collocated and staggered grid. As the second contribution, we present a novel method for the simulation of thin shells with frictional contact using a combination of MPM and subdivision finite elements. The shell kinematics are assumed to follow a continuum shell model which is decomposed into a Kirchhoff-Love motion that rotates the mid-surface normals followed by shearing and compression/extension of the material along the mid-surface normal. We use this decomposition to design an elastoplastic constitutive model to resolve frictional contact by decoupling resistance to contact and shearing from the bending resistance components of stress. We show that by resolving frictional contact with a continuum approach, our hybrid Lagrangian/Eulerian approach is capable of simulating challenging shell contact scenarios with hundreds of thousands to millions of degrees of freedom. Without the need for collision detection or resolution, our method runs in a few minutes per frame in these high-resolution examples. Furthermore, we show that our technique naturally couples with other traditional MPM methods for simulating granular and related materials. In the third part, we present a new hybrid Lagrangian Material Point Method for simulating volumetric objects with frictional contact. The resolution of frictional contact in the thin shell simulation cannot be generalized to the case of volumetric materials directly. Also, even though MPM allows for the natural simulation of hyperelastic materials represented with Lagrangian meshes, it usually coarsens the degrees of freedom of the Lagrangian mesh and can lead to artifacts, e.g., numerical cohesion. We demonstrate that our hybrid method can efficiently resolve these issues. We show the efficacy of our technique with examples that involve elastic soft tissues coupled with kinematic skeletons, extreme deformation, and coupling with various elastoplastic materials. Our approach also naturally allows for two-way rigid body coupling.

The Material Point Method for the Physics based Simulation of Solids and Fluids

The Material Point Method for the Physics based Simulation of Solids and Fluids Book
Author : Chenfanfu Jiang
Publisher : Unknown
Release : 2015
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Simulating fluids and solid materials undergoing large deformation remains an important and challenging problem in Computer Graphics. The dynamics of these materials usually involve dramatic topological changes and therefore require sophisticated numerical approaches to achieve sufficient accuracy and visual realism. This dissertation focuses on the Material Point Method (MPM) for simulating solids and fluids for use in computer animation, and it makes four major contributions: First, we introduce new MPM for simulating viscoelastic fluids, foams and sponges. Our second contribution is to introduce a novel technique designed to retain the stability of the original PIC, without suffering from the noise and instability of FLIP. Our third contribution is to introduce a novel material point method for heat transport, melting and solidifying materials. Our fourth contribution is to show that recasting the backward Euler method as a minimization problem allows Newton's method to be stabilized by standard optimization techniques with some novel improvements of our own.

A Material Point Method for Simulating Frictional Contact with Diverse Materials

A Material Point Method for Simulating Frictional Contact with Diverse Materials Book
Author : Xuchen Han
Publisher : Unknown
Release : 2020
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

We present an extension to the Material Point Method (MPM) for simulating elastic objects with various co-dimensions like hair (1D), thin shells (2D), and volumetric objects (3D). We simulate thin shells with frictional contact using a combination of MPM and subdivision finite elements. The shell kinematics are assumed to follow a continuum shell model which is decomposed into a Kirchhoff-Love motion that rotates the mid-surface normals followed by shearing and compression/extension of the material along the mid-surface normal. We use this decomposition to design an elastoplastic constitutive model to resolve frictional contact by decoupling resistance to contact and shearing from the bending resistance components of stress. We show that by resolving frictional contact with a continuum approach, our hybrid Lagrangian/Eulerian approach is capable of simulating challenging shell contact scenarios with hundreds of thousands to millions of degrees of freedom. Furthermore our technique naturally couples with other traditional MPM methods for simulating granular materials. Without the need for collision detection or resolution, our method runs in a few minutes per frame in these high resolution examples. For the simulation of hair and volumetric elastic objects, we utilize a Lagrangian mesh for internal force computation and an Eulerian mesh for self collision as well as coupling with external materials. While the updated Lagrangian discretization where the Eulerian grid degrees of freedom are used to take variations of the potential energy is effective in simulating thin shells, its frictional contact response strategy does not generalize to volumetric objects. Therefore, we develop a hybrid approach that retains Lagrangian degrees of freedom while still allowing for natural coupling with other materials simulated with traditional MPM. We demonstrate the efficacy of our technique with examples that involve elastic soft tissues coupled with kinematic skeletons, extreme deformation, and coupling with multiple elastoplastic materials. Our approach also naturally allows for two-way rigid body coupling.

The Material Point Method for Simulating Elastoplastic Materials

The Material Point Method for Simulating Elastoplastic Materials Book
Author : Chuyuan Fu
Publisher : Unknown
Release : 2018
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Simulation in computer graphics must accommodate a wide range of material behaviors under large deformation, topological changes, contact or collision. This dissertation focuses on hybrid Lagrangian/Eulerian methods, especially the Material Point Method (MPM) in computer animation, and we list the major contributions here: First, we simulate sand dynamics using an elastoplastic, continuum assumption. We demonstrate that the Drucker-Prager plastic flow model combined with a Hencky-strain-based hyperelasticity accurately recreates a wide range of visual sand phenomena with moderate computational expense. The Drucker-Prager model naturally represents the frictional relation between shear and normal stresses through a yield stress criterion. We develop a stress projection algorithm used for enforcing this condition with a non-associative flow rule. We further extend the idea of simulating sand dynamics using an elastoplastic continuum assumption to codimensional objects. Our second contribution is to introduce a novel method for simulation of thin shells with frictional contact using a combination of the MPM and subdivision finite elements. The shell kinematics are assumed to follow a continuum shell model which is decomposed into a Kirchhoff-Love motion that rotates the mid-surface normals followed by shearing and compression/extension of the material along the mid-surface normal. We use this decomposition to decouple resolving contact and shearing from the bending resistance components of stress. Our approach is capable of simulating challenging shell contact scenarios with hundreds of thousands to millions of degrees of freedom with a moderate cost of only a few minutes per frame. Our third contribution is to introduce a novel transfer scheme for hybrid Lagrangian/Eulerian simulations. Recently the Affine Particle-In-Cell (APIC) Method was introduced to improve the accuracy of the transfers in Particle-In-Cell (PIC) without suffering from the noise present in the historic alternative, Fluid-Implicit-Particle (FLIP). We generalize APIC by augmenting each particle with a more general local function. Our transfers are designed to select particle-wise polynomial approximations to the grid velocity that are optimal in the local mass-weighted $L^2$ norm. With only marginal additional cost, our generalization improves kinetic energy conservation during transfers which leads to better vorticity resolution in fluid simulations and less numerical damping in elastoplasticity simulations.

A Material Point Method for Complex Fluids

A Material Point Method for Complex Fluids Book
Author : Daniel Ram
Publisher : Unknown
Release : 2015
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

We present a novel Material Point Method for simulating complex materials. The method achieves plasticity effects via the temporal evolution of the left elastic Cauchy-Green strain. We recast the upper-convected derivative of the strain in the Oldroyd-B constitutive model as a plastic flow and are able to simulate elastic and viscoelastic effects. Our model provides a volume-preserving rate-based description of plasticity that does not require singular value decompositions. Our semi-implicit discretization allows for high-resolution simulations. We also present novel discretizations of the temporal update of the left elastic Cauchy-Green strain for several constitutive models that preserve symmetry and positive-definiteness of the strain for use in the Material Point Method. A novel modification to a constitutive model is also presented that models material softening under plastic compression.

Development of Modifications to the Material Point Method for the Simulation of Thin Membranes Compressible Fluids and Their Interactions

Development of Modifications to the Material Point Method for the Simulation of Thin Membranes  Compressible Fluids  and Their Interactions Book
Author : Anonim
Publisher : Unknown
Release : 2001
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

The material point method (MPM) is an evolution of the particle in cell method where Lagrangian particles or material points are used to discretize the volume of a material. The particles carry properties such as mass, velocity, stress, and strain and move through a Eulerian or spatial mesh. The momentum equation is solved on the Eulerian mesh. Modifications to the material point method are developed that allow the simulation of thin membranes, compressible fluids, and their dynamic interactions. A single layer of material points through the thickness is used to represent a membrane. The constitutive equation for the membrane is applied in the local coordinate system of each material point. Validation problems are presented and numerical convergence is demonstrated. Fluid simulation is achieved by implementing a constitutive equation for a compressible, viscous, Newtonian fluid and by solution of the energy equation. The fluid formulation is validated by simulating a traveling shock wave in a compressible fluid. Interactions of the fluid and membrane are handled naturally with the method. The fluid and membrane communicate through the Eulerian grid on which forces are calculated due to the fluid and membrane stress states. Validation problems include simulating a projectile impacting an inflated airbag. In some impact simulations with the MPM, bodies may tend to stick together when separating. Several algorithms are proposed and tested that allow bodies to separate from each other after impact. In addition, several methods are investigated to determine the local coordinate system of a membrane material point without relying upon connectivity data.

The Numerical Prediction of Material Failure Based on the Material Point Method

The Numerical Prediction of Material Failure Based on the Material Point Method Book
Author : Shijian Zhou
Publisher : Unknown
Release : 1998
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download The Numerical Prediction of Material Failure Based on the Material Point Method book written by Shijian Zhou, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

A Material Point Method for Elastoplasticity with Ductile Fracture and Frictional Contact

A Material Point Method for Elastoplasticity with Ductile Fracture and Frictional Contact Book
Author : Stephanie Wang
Publisher : Unknown
Release : 2020
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Simulating physical materials with dynamic movements to photo-realistic resolution has always been one of the most crucial and challenging topics in Computer Graphics. This dissertation considers large-strain elastoplasticity theory applied to the low-to-medium stiffness regime, with topological changes and codimensional objects incorporated. We introduce improvements to the Material Point Method (MPM) for two particular objectives, simulating fracturing ductile materials and incorporation of MPM and Lagrangian Finite Element Method (FEM). Our first contribution, simulating ductile fracture, utilizes traditional particle-based MPM [SSC13, SCS94] as well as the Lagrangian energy formulation of [JSS15] which uses a tetrahedron mesh, rather than particle-based estimation of the deformation gradient and potential energy. We model failure and fracture via elastoplasticity with damage. The material is elastic until its deformation exceeds a Rankine or von Mises yield condition. At that point, we use a softening model that shrinks the yield surface until it reaches the damage thresh- old. Once damaged, the material Lam e coefficients are modified to represent failed material. This approach to simulating ductile fracture with MPM is successful, as MPM naturally captures the topological changes coming from the fracture. However, rendering the crack surfaces can be challenging. We design a novel visualization technique dedicated to rendering the material's boundary and its intersection with the evolving crack surfaces. Our approach uses a simple and efficient element splitting strategy for tetrahedron meshes to create crack surfaces. It employs an extrapolation technique based on the MPM simulation. For traditional particle-based MPM, we use an initial Delaunay tetrahedralization to connect randomly sampled MPM particles. Our visualization technique is a post-process and can run after the MPM simulation for efficiency. We demonstrate our method with several challenging simulations of ductile failure with considerable and persistent self-contact and applications with thermomechanical models for baking and cooking. Our second contribution, hybrid MPM-Lagrangian-FEM, aims to simulate elastic objects like hair, rubber, and soft tissues. It utilizes a Lagrangian mesh for internal force computation and a Eulerian grid for self-collision, as well as coupling with external materials. While recent MPM techniques allow for natural simulation of hyperelastic materials represented with Lagrangian meshes, they utilize an updated Lagrangian discretization and use the Eulerian grid degrees of freedom to take variations of the potential energy. It often coarsens the degrees of freedom of the Lagrangian mesh and can lead to artifacts. We develop a hybrid approach that retains Lagrangian degrees of freedom while still allowing for natural coupling with other materials simulated with traditional MPM, e.g., sand, snow, etc. Furthermore, while recent MPM advances allow for resolution of frictional contact with codimensional simulation of hyperelasticity, they do not generalize to the case of volumetric materials. We show that our hybrid approach resolves these issues. We demonstrate the efficacy of our technique with examples that involve elastic soft tissues coupled with kinematic skeletons, extreme deformation, and coupling with various elastoplastic materials. Our approach also naturally allows for two-way rigid body coupling.

Multi material Simulation with the Material Point Method

Multi material Simulation with the Material Point Method Book
Author : Alexander Maximilian Nilles
Publisher : Unknown
Release : 2020
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Multi material Simulation with the Material Point Method book written by Alexander Maximilian Nilles, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Validation and Applications of the Material Point Method

Validation and Applications of the Material Point Method Book
Author : Ali Tabatabaeian Nimavardi
Publisher : Unknown
Release : 2017
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Validation and Applications of the Material Point Method book written by Ali Tabatabaeian Nimavardi, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Multiphase Simulation Using Material Point Method

Multiphase Simulation Using Material Point Method Book
Author : Andre Pradhana
Publisher : Unknown
Release : 2017
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

We present a discussion on how one can simulate sand as a continuum using elastoplasticity. We showed the efficacy of Drucker-Prager plasticity model and St. Venant Kirchhoff with Hencky strain to model sand. We discretized the continuum equation using Material Point Method (MPM). We also present a multi-species model for the simulation of gravity driven landslides and debris flows with porous sand and water interactions. We use continuum mixture theory to describe individual phases where each species individually obeys conservation of mass and momentum and they are coupled through a momentum exchange term. Water is modeled as a weakly compressible fluid and sand is modeled with an elastoplastic law whose cohesion varies with water saturation. We use Material Point Method to discretize the governing equations. We use two grids, corresponding to water and sand phase. The momentum exchange term in the mixture theory is relatively stiff and we use semi-implicit time stepping to avoid associated small time steps. Our semi-implicit treatment is explicit in plasticity and preserves symmetry of force linearizations. We develop a novel regularization of the elastic part of the sand constitutive model that better mimics plasticity during the implicit solve to prevent numerical cohesion artifacts that would otherwise have occurred. Lastly, we develop an improved return mapping for sand plasticity that prevents volume gain artifacts in the traditional Drucker-Prager model. Finally, we revisit the problem of redistancing, which is native to the level set paradigms. We used an interesting alternative view that utilizes the Hopf-Lax formulation of the solution to the eikonal equation, as proposed by \cite{lee:2017:revisiting,darbon:2016:algorithms}. In this approach, the signed distance at an arbitrary point is obtained without the need of distance information from neighboring points. We extend the work of Lee et al. \cite{lee:2017:revisiting} to redistance functions defined via interpolation over a regular grid.

Formulation of a Dynamic Material Point Method MPM for Geomechanical Problems

Formulation of a Dynamic Material Point Method  MPM  for Geomechanical Problems Book
Author : Issam K. J. al- Kafaji
Publisher : Unknown
Release : 2013
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Formulation of a Dynamic Material Point Method MPM for Geomechanical Problems book written by Issam K. J. al- Kafaji, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Simulation of Granular Media with the Material Point Method

Simulation of Granular Media with the Material Point Method Book
Author : Gergely Klar
Publisher : Unknown
Release : 2016
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

We propose an extension to the Material Point Method for the simulation of granular media. We model the dynamics with an elastoplastic, continuum assumption. The behavior of the granular media is captured by the Drucker-Prager yield criterion that naturally represents the frictional relationship between shear and normal stresses. We develop a stress projection algorithm that is well suited for both explicit and implicit time integration, and uses a non-associative flow rule to ensure volume preservation. Our approach is able to recreate the dynamics of granular media undergoing large deformations, topological changes, and collisions.

Splitting Solution Scheme for Material Point Method

Splitting Solution Scheme for Material Point Method Book
Author : Shyamini Kularathna
Publisher : Unknown
Release : 2018
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Splitting Solution Scheme for Material Point Method book written by Shyamini Kularathna, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Material Point Method for Modelling Additive Manufacturing

Material Point Method for Modelling Additive Manufacturing Book
Author : Hai Yan
Publisher : Unknown
Release : 2019
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Material Point Method for Modelling Additive Manufacturing book written by Hai Yan, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Material Point Method to Simulate Large Deformation Problems in Fluid saturated Granular Medium

Material Point Method to Simulate Large Deformation Problems in Fluid saturated Granular Medium Book
Author : Samila Sanjeevanie Bandara
Publisher : Unknown
Release : 2013
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Material Point Method to Simulate Large Deformation Problems in Fluid saturated Granular Medium book written by Samila Sanjeevanie Bandara, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.