6th MPM Workshop
University of New Mexico
Albuquerque, NM 87131
August 9-10, 2010
Affiliation: Wasatch Molecular, Inc
Email: bard@wasatchmolecular.com
Presentation Title: Dynamic Fracture Simulations in MPM using a J-Integral Approach (pdf)
Abstract: Fracture is an important aspect of material response, often resulting in structural degradation or failure. Realistic initial flaw distributions and their evolution are exceedingly difficult to characterize experimentally. Numerical simulations may provide a practical avenue to obtain insight into complex fracture problems beyond current capabilities to explore experimentally.
Cohesive zones are a promising computational technique that has recently received substantial attention in the simulation of fracture propagation. While clearly a general concept for modeling the separation of surfaces, its typical implementation relies on selecting possible fracture path(s) in advance. In the FEM the cohesive zones are placed between elements, further constraining fracture path(s) to be along mesh lines. In the MPM particles may be used to define cohesive zones independent of the computational mesh, but these still must be defined in advance in the absence of propagation criteria. Here the calculation of crack tip J-integrals is used to determine the critical energy release rate needed for dynamic fracture propagation. The J-integral must be generalized for dynamic scenarios and a volume integral is required for path independence. A variety of criteria may be used to determine propagation direction. With the presence of an explicit fracture tip and propagation criteria, cohesive zones may be introduced only as needed to define new fracture surfaces as the crack tip propagates. This combination provides a very general framework in which to handle fracture propagation and model a variety of crack opening physics, including frictional sliding and process zones. The methods are illustrated via examples.
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Affiliation: Deltares / University of Stuttgart
Email: Lars.Beuth@deltares.nl
Presentation Title: Application of a Quasi-Static Material Point Method in Geomechanics (pdf)
Abstract: In geomechanics various quasi-static processes like the installation of jacked piles involve heavy deformations of soil. In order to facilitate the analysis of such large deformation problems, a quasi-static Material Point Method making use of an implicit integration scheme is being developed in the frame of a EU funded research project.
Results of the simulation of cone penetration testing in cohesive material under undrained conditions will be presented. Here, the underlying finite element mesh consists of 4-noded tetrahedral elements. Smooth, adhesive and rough contact between soil and penetrometer are considered by means of interface elements.
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Affiliation: University of Utah
Email: Rebecca.Brannon@utah.edu
Presentation Title: Title: Convected particle domain interpolation (CPDI) method.
A. Sadeghirad (alireza.sadeghirad@utah.edu), R.M. Brannon (Rebecca.Brannon@utah.edu), J. Burghardt (j.burghardt@utah.edu)
Abstract: A new algorithm to improve accuracy and efficiency of the material point method for problems involving extremely large tensile deformations and rotations is presented. In the new procedure, particle domains are convected with the material motion more accurately than in the generalized interpolation material point (GIMP) method. Each particle domain is treated as a parallelogram that deforms with the material and which is evolved (optionally to high-order accuracy) assuming that the velocity gradient is constant over the time step. An approximation of the grid basis function over the particle domain is constructed using a standard 4-node finite-element interpolation of the actual grid basis function on the convected parallelogram. Verification examples are presented to demonstrate the robustness and accuracy of the new algorithm in comparison to both the generalized interpolation material point (GIMP) method and the standard material point method (MPM), both of which fail from a spurious tensile instability long before significant deformation develops. A more complicated 2D generalized vortex ring verification problem is designed using the Method of Manufactured Solutions to induce varying degrees of simple shear with variable amounts of superimposed rotation at all times and at all spatial locations. The motion is chosen to induce material motion inside a ring (i.e., plane strain cylinder). The manufactured displacement field has a zero gradient at and beyond the boundary of the ring, thus giving a Neumann problem for which enforcement of boundary conditions is trivial. This manufactured solution is appealing to verify basis and frame indifference of complicated nonlinear (even path dependent) constitutive models -– all that is needed is a function for the material response under simple shear without superimposed rotation. Errors in the host code’s momentum and kinematics solvers can be separately assessed under arbitrarily large deformation by using a simplistic material model such a neo-Hookean elasticity.
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Affiliation: University of Missouri
Email: chenzh@missouri.edu
Presentation Title: A Comparative Study on Impact Failure Evolution with the MPM and MD (pdf)
Abstract: A Comparative Study on Impact Failure Evolution with the MPM and MD
Zhen Chen and Shan Jiang, Department of Civil and Environmental Engineering
University of Missouri, Columbia, MO 65211, USA
Yong Gan, Department of Engineering Mechanics
Zhejiang University, Hangzhou, Zhejiang 310027, China
Thomas D. Sewell and Donald L. Thompson, Department of Chemistry
University of Missouri, Columbia, MO 65211, USA
Corresponding Email: chenzh@missouri.edu
A hierarchical and concurrent model-based simulation procedure coupled via a nonlocal approach is being developed for predicting the spatial-temporal energy release properties of aluminum-based metastable intermolecular composites. As one of the research tasks, multi-scale evolution of failure under impact loading must be understood and modeled with appropriate constitutive equations. With the use of the Material Point Method (MPM) and molecular dynamics (MD) simulation, a comparative study has recently been performed to investigate the effects of aspect ratio, boundary conditions, loading types, problem geometry and size on impact failure evolution at different scales. The preliminary results and future directions will be discussed in this workshop.
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Affiliation: Schlumberger
Email: james.guilkey@utah.edu
Presentation Title: Use of Uintah MPM-ICE to Investigate the Efficacy of Seismic Air-Guns for Coalbed Fracturing
Abstract: It has been proposed that a series of air-guns, such as those used as downhole seismic sources, could be applied to open up the naturally occurring cleats found in coalbeds. To the extent that these cleats remain open following stimulation, they would provide a series of conduits for extraction of methane gas. In this report, the possibility of achieving this goal is investigated in the context of a particular air-gun and a particular reservoir, with sensitivity to certain parameters also considered. Numerical simulations are carried out using the Uintah package for fluid-structure interaction. Results from the numerical simulations are presented which indicate the amount of relative motion across cleat interfaces for each of the cases considered. In addition, a simple analytical solution based on energy balance is also used to support the findings of the numerical modeling. While the numerical results are specific to this system, the analytical solution provides some general guidance for considering other configurations in the future.
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Affiliation: Oregon State Unversity
Email: edward.le@oregonstate.edu
Presentation Title: MPM Simulation of Wood-Strand Composites (ppt)
Abstract: In wood-based composites, the glue-line (interface) between wood-strands affects the stress transfer from one member to the next. The glue-line properties determine the rate of load transfer between phases and these properties depend on wood species, surface preparation, glue properties, glue penetration into wood cells, and moisture content of the wood. As a result, the strength and stiffness of the composites are significantly affected by the amount, distribution, and properties of the resin.
In the first part of this study, the glue-line stiffness between wood strands was determined by experiments. The interfacial properties were calculated from experimental data on double lap shear (DLS) specimens. The results showed that in both normal and densified wood strands, resin coverage has a positive effect on the interfacial stiffness, and consequently on stiffness properties of wood-based composites. As adhesive coverage increased from discrete droplets (1% coverage) to a continuous bondline (100% or fully glued) the stiffness of the interface increased significantly and could even become stiffer than the wood itself.
In the second part of this study, once the mechanical properties of individual strands and interfacial properties were determined by experiment, they were then used as an input to a numerical model for the mechanical properties of oriented strand board (OSB) panels. Modeling the compression of wood-strands and wood-based composites was done using a numerical method called the material point method (MPM). MPM was used to model wood-strand composite mechanical properties as a function of compaction (densification), compaction rate, strand geometry (strand length and strand size), strand undulations, strand properties, and adhesive properties. In addition, the density profiles of the panels as a function of selected properties were studied. The various simulations were for either conventional OSB panels or for OSB panels with densified strands in the surface layers.
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Affiliation: University of Alaska Fairbanks
Email: jonah.lee@alaska.edu
Presentation Title: A Few MPM Verification Problems Using Uintah (pdf)
Abstract: The Material Point Method offers ample opportunities for tackling complicated problems that are not amenable to traditional computational methods such as the finite element method. The parallel code Uintah provides a practical and sophisticated tool to solve these
problems. Verification of computational codes for intended purposes is important to gain confidence of the underlying method as well as
the codes themselves. The purpose of this talk is to present a few MPM verification problems using Uintah in solid mechanics, fluid mechanics, and fluid-structure interaction.
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Affiliation: Los Alamos National Laboratory
Email: xia@lanl.gov
Presentation Title: Transfer Coefficient Algorithm for Small Mass Nodes in Material Point Method (ppsx)
Abstract: One of the advantages of the Material Point Method (MPM) is its capability to simulate large material deformation without the need to advect state variables, such as stress and strain of the material through an Eulerian mesh. MPM can keep sharp interface without smearing them due to numerical diffusion associated with such advection. MPM also avoids distortion and entanglement of meshes associated with a Lagrange method in the case of a large deformation. However, the straightforward MPM also has its own disadvantages. When a material point just enters a new cell, it can cause a very small mass on the nodes far from the material point in the cell. As denominator in the calculation of acceleration, this small mass can cause numerical instability and leads to artificially large acceleration. The present work deals with this numerical instability by transferring the force away from the small mass nodes in a manner consistent with the error of the MPM calculation. This treatment significantly improves the stability of the simulation.
The numerical cost of this algorithm is negligible considering the computational time saved by the significantly increased time step size. We provide comparisons between the results calculated with and without this improvement to MPM.
release number: LA-UR 10-04280
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Affiliation: University of Washington
Email: pmackenz@uw.edu
Presentation Title: Locking effects in the MPM (pdf)
Abstract: A typical MPM background grid and Q4/B8 Finite elements share the same shape functions. While this similarity is beneficial for coupling of MPM and FEM, MPM also inherits locking problems well known within the FEM. Moreover, cell crossings introduce another locking mechanism, unknown to the FEM. The presentation will discuss sources of different locking mechanisms and propose simple mitigation techniques for the MPM.
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Affiliation: University of Washington
Email: cmast@u.washington.edu
Presentation Title: Representing arbitrary bounding surfaces in the MPM (pdf)
Abstract: In many MPM applications, a uniform, rectangular background grid is used to solve the governing equations. While the use of such a grid is convenient and efficient from an implementation standpoint, it limits the method’s ability impose essential boundary conditions at arbitrary locations within the computational domain. This presentation will introduce a strategy for incorporating general surface geometries while by and large maintaining the use of a uniform, rectangular grid.
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Affiliation: Monash University
Email: louis.moresi@monash.edu
Presentation Title: Geoscience applications of Material Point Methods
Abstract: We have made extensive use of Material-Point-like methods in modelling large-scale tectonic processes which are characterised by very large deformation (including solid-state convection), free surfaces with erosion and sedimentation, and a multiplicity of mineral phase transitions. The governing equations for our problems are creeping viscous / viscoelastic flow with very strong variations in the material coefficients which develop due to material contrasts, deformation history and non-linear dependence upon the stress/strain rate.
We use an implicit formulation for the determination of the primary unknowns (the fluid velocity field) for which an implicit solver using a structured grid geometry, a pre-determined parallel decomposition and geometrical multigrid is the principle attraction of the Material Point Method. Despite these advantages, there are a number of difficulties which we encounter in using a particle-based integration scheme which we will briefly discuss.
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Affiliation: Department of Mechanical Engineering, University of Utah
Email: a.srad@yahoo.com
Presentation Title: A method for analyzing weak discontinuities based on the convected particle domain interpolation (CPDI) method.
A. Sadeghirad (alireza.sadeghirad@utah.edu), R.M. Brannon (Rebecca.Brannon@utah.edu), J.E. Guilkey(James.Guilkey@m.cc.utah.edu).
Abstract: An extension of the newly developed convected particle domain interpolation, named CPDI2, is introduced to track the particle domains as quadrilaterals. The CPDI2 is more flexible than the original CPDI for discretization of complex geometries, especially in the vicinity of abutting material boundaries where weak discontinuities call for local spatial refinement. A new algorithm is presented for extension of the CPDI2 method to the problems involving weak discontinuities that are not necessarily aligned with grid cell boundaries. In the proposed technique, weak discontinuities across the interfaces are handled by adding extra degrees of freedom. These additional degrees of freedom are assigned to the corners of the quadrilateral particle domains that are at or near the interface. At each time step, the equations of motion are solved for these additional degrees of freedom as well as degrees of freedom associated with the grid nodes. One-dimensional and two-dimensional examples demonstrate the effectiveness of the proposed procedure.
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Affiliation: UNM
Email: jsanche1@unm.edu
Presentation Title: A Critical Evaluation of Computational Fracture Using a Smeared Crack Approach in MPM (pdf)
Abstract: TBD
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Affiliation: Jveer Aerospace Ltd.
Email: jveer@jveer.com
Presentation Title: Introducing MPMsim: a material point method alternative to traditional FEA explicit dynamics
Abstract: This presentation will introduce a new simulation and analysis tool that uses a modified version of the material point method to solve engineering problems. More information can be found at www.mpmsim.com. The presentation will also include results from investigating the effect of different convergence parameters on simulation results.
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Affiliation: University of New Mexico
Email: wallstedt@yahoo.com
Presentation Title: An Application of Uncertainty Quantification to MPM (pdf)
Abstract: Uncertainty Quantification has become a major research focus in simulation science. A brief overview of UQ is presented, and a simple method of UQ analysis - Latin Hypercube Sampling - is applied to a MPM model of a cantilever beam. The UQ application exposes a long-hidden bug in the author's MPM code, and also demonstrates an important factor in the beam model that had not been considered previously.
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Affiliation: ACTA Inc.
Email: wathugala@actainc.com
Presentation Title: Applications of MPM to material breakup.
Abstract: TBD
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Affiliation: Los Alamos National Laboratory
Email: dzhang@lanl.gov
Presentation Title: Continuous Gradient Method to Cell Crossing Instability (pdf)
Abstract: Although the material point method has been used to study material interactions with large deformation, the instability caused by material points move across mesh cells is still an issue
hampering efficient application of the method. Especially when the material point method is used to calculated brittle damages to materials, the instability can cause premature break of the materials. This cell crossing instability originates from the discontinuity of the gradient of the shape function in the material point.
In this work we present a numerical scheme that redefines the gradient of the shape function. The
redefined gradient of the shape function is continuous and mathematically consistent with the
fundamental solution method to the partial differential equation, namely the weak solution principle. The use of this redefined gradient eliminates the cell crossing instability. The new method is proved to conserve momentum. The energy dissipation is proved to be second order in both the spatial and the temporal discretization. Numerical examples are provided to shown the improved stability and accuracy of the newly improved method.
ABSTRACTS :