Tag Archives: MPM
Publication (Abstract and Erratum): Second-order convected particle domain interpolation (CPDI2) with enrichment for weak discontinuities at material interfaces
Abstract:
Convected particle domain interpolation (CPDI) is a recently developed extension of the material point method, in which the shape functions on the overlay grid are replaced with alternative shape functions, which (by coupling with the underlying particle topology) facilitate efficient and algorithmically straightforward evaluation of grid node integrals in the weak formulation of the governing equations. In the original CPDI algorithm, herein called CPDI1, particle domains are tracked as parallelograms in 2-D (or parallelepipeds in 3-D). In this paper, the CPDI method is enhanced to more accurately track particle domains as quadrilaterals in 2-D (hexahedra in 3-D). This enhancement will be referred to as CPDI2. Not only does this minor revision remove overlaps or gaps between particle domains, it also provides flexibility in choosing particle domain shape in the initial configuration and sets a convenient conceptual framework for enrichment of the fields to accurately solve weak discontinuities in the displacement field across a material interface that passes through the interior of a grid cell. The new CPDI2 method is demonstrated, with and without enrichment, using one-dimensional and two-dimensional examples.
Bib data:
Sadeghirad, A., R. M. Brannon, J.E. Guilkey (2013) Second-order convected particle domain interpolation (CPDI2) with enrichment for weak discontinuities at material interfaces, Int. J. Num. Meth. Engr., vol. 95, 928-952
URL: http://dx.doi.org/10.1002/nme.4526
Bibtex entry:
@ARTICLE{Sadeghirad2013,
author = {A. Sadeghirad and R.M. Brannon and J.E. Guilkey},
title = {Second-order convected particle domain interpolation ({CPDI2}) with
enrichment for weak discontinuities at material interfaces},
journal = {Intl. J. Num. Meth. Engng.},
year = {2013},
volume = {95},
pages = {928–952}
}
Erratum: Eq. 33 should be
Uintah Simulations of Perforation Experiments
ABSTRACT: A simulation of a simple penetration experiment is performed using Material Point Method (MPM) through the Uintah Computational Framework (UCF) and interpreted using the post-processing visualization program VisIt. MPM formatting sets a background mesh with explicit boundaries and monitors the interaction of particles within that mesh to predict the varying movements and orientations of a material in response to loads. The modeled experiment compares the effects of an aluminum sphere impacting an aluminum sheet at varying velocities. In this work, the experiment called launch T-1428 (by Piekutowski and Poorman) is simulated using UCF and VisIt. The two materials in the experiment are both simulated using a hypoelastic-plastic model. Varying grid resolutions were used to verify the convergent behavior of the simulations to the experimental results. The validity of the simulation is quantified by comparing perforation hole diameter. A full 3-D simulation followed and was also compared to experimental results. Results and issues in both 2-D and 3-D simulation efforts are discussed. Both the axisymmetric and 3-D simulation results provided very good data with clear convergent behavior.
See the link below for the full report.
Abstract: Deformation and Fracture of Heterogeneous Media using Boundary-Conforming Convected Particle Characteristic Functions in the Material Point Method
This is an abstract for
NWU2013: Advances in Computational Mechanics with Emphasis on Fracture and Multiscale Phenomena. Workshop honoring Professor Ted Belytschko’s 70th Birthday. April 18, 2013 – April 20, 2013, Evanston, IL, USA
The organizers allocated only 10 minutes for each person’s talk (including big wigs like Tom Hughes), so we might just present this topic in the form of a puppet show with enough information to tickle the audience to chat with us about it in the hallway!
Authors:
Rebecca Brannon*, Alireza Sadeghirad, James Guilkey
Department of Mechanical Engineering
University of Utah
Salt Lake City, UT, 84112
*Email: Rebecca.Brannon@utah.edu
Abstract: Simulation of Buried Explosives
Click here to see an invited talk for the 2013 Advances in Computational Mechanics Conference celebrating the 70th birthday of Thomas J.R. Hughes.
Research: Weibull fragmentation in the Uintah MPM code
Tough disk impacting brittle disk
Below are links to two simulations of disks colliding. The first is elastic and the second uses a fracture model with spatially variable strength based on a scale-dependent Weibull realization. Both take advantage of the automatic contact property of the MPM.
WeibConstMovie: disks colliding without fracture
WeibPerturbedGood: disks colliding with heterogeneous fracture
This basic capability to support statistically variable strength in a damage model has been extended to the Kayenta plasticity model in Uintah.
Publication: Application of Uintah-MPM to shaped charge jet penetration of aluminum
J. Burghardt, B. Leavy, J. Guilkey, Z. Xue, R. Brannon
The capability of the generalized interpolation material point (GIMP) method in simulation of penetration events is investigated. A series of experiments was performed wherein a shaped charge jet penetrates into a stack of aluminum plates. Electronic switches were used to measure the penetration time history. Flash x-ray techniques were used to measure the density,length, radius and velocity of the shaped charge jet. Simulations of the penetration event were performed using the Uintah MPM/GIMP code with several different models of the shaped charge jet being used. The predicted penetration time history for each jet model is compared with the experimentally observed penetration history. It was found that the characteristics of the predicted penetration were dependent on the way that the jet data are translated to a discrete description. The discrete jet descriptions were modified such that the predicted penetration histories fell very close to the range of the experimental data. In comparing the various discrete jet descriptions it was found that the cumulative kinetic energy flux curve represents an important way of characterizing the penetration characteristics of the jet. The GIMP method was found to be well suited for simulation of high rate penetration events.
Available Online:
http://iopscience.iop.org/1757-899X/10/1/012223
http://www.mech.utah.edu/~brannon/pubs/7-2010BurghardtLeavyGuilkeyXueBrannon_ApplicMPMshapedCharge.pdf
CPDI shape functions for the Material Point Method
In a conventional MPM formulation, the shape functions on the grid are the same as in a traditional FEM solution. In the CPDI, the shape functions on the grid are replaced by alternative (and still linearly complete*) shape functions, given by piecewise linear interpolations of the traditional FEM shape functions to the boundaries of the particles. This change provides FEM-level accuracy in moderately deforming regions while retaining the attractive feature of MPM that particles can move arbitrarily relative to one another in massively deforming regions (provided, of course, that the deformation is updated in a manner compatible with the constitutive model).
In the images below, the shaded regions are the traditional FEM “tent” linear shape functions in 1-D, and the solid lines are the CPDI interpolated shape functions, which clearly change based on particle position relative to the grid. Both the traditional FEM tent functions and these new CPDI functions are linearly complete (i.e., they can exactly fit any affine function). The tremendous advantage of CPDI is that the basis functions are extraordinarily simple over a particle domain, thus facilitating exact and efficient evaluation of integrals over particle domains.
University of Utah CSM Group 