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Army High Performance Computing Research Center

WORKSHOP ON COMPUTATIONAL METHODS FOR PROBLEMS WITH

EVOLVING DOMAINS AND DISCONTINUITIES

PROGRAM

STANFORD UNIVERSITY

DECEMBER 3-5, 2013

  Workshop Program Tuesday, December 3

       

Date Start Time End Time Function Room 12/03/2013 6:30 pm Bus Pick-up at Guest

house

7:00 pm 9:00 pm Reception & Dinner Zibibbo , Palo Alto 12/04/2013 7:30 am 8:00 am Registration and

Breakfast Kavli Auditorium lobby

8:00 am 12:20 pm Sessions Kavli Auditorium 12:25 pm 1:45 pm Buffet Lunch Kavli Auditorium 1:45 pm 5:55 pm Session Kavli Auditorium 6:30 pm Bus pick up at Guest

house

7:00 pm 9:00 pm Dinner Trellis, Menlo Park 12/05/2013 8:20 am 8:50 am Breakfast Kavli Auditorium lobby

8:50 am 12:25 pm Sessions Kavli Auditorium 12:25 pm 1:40 pm Buffet Lunch Kavli Auditorium 1:40 pm 6:00 pm Session & Summary Kavli Auditorium

12/05/2013 6:30 pm Bus pick up at Guest House

7:00 pm 9:00 pm Dinner Café del Sol, Menlo Park

TUESDAY – December 3 6:30 – 7:00 Bus pick-up at Stanford Guest House 7:00 – 9:00 Welcome Dinner- Zibibbo Welcome and Orientation 430 Kipling Street Charbel Farhat & Adrian Lew Palo Alto, CA 94301

 Workshop Program

Wednesday, December 4    

7:30 – 8:00 Registration at Kavli Lobby

Continental Breakfast available

8:00 – 8:10 Welcome Remarks Farhat, Zohdi, Lew Session on Multi-Material Flows Chair: Tarek Zohdi 8:10 – 8:45 Lagrangian frames: an efficient and Sergio Idelsohn,

accurate way to solve multi-fluids flows Universitat Politècnica de Catalunya

8:50 – 9:25 ReALE reconnection-based arbitrary Mikhail Shashkov, Lagrangian Eulerian method for Los Alamos National

multi -material hydrodynamics Laboratory 9:30 - 10:05 The FIVER framework for compressible Charbel Farhat, Stanford multi-material problems University 10:05 – 10:25 Break Session on Fluid-Structure Interaction Chair: Adrian Lew 10:25 – 11:00 An embedded boundary method Wolfgang Wall,

designed for complex fluid-structure Technische interaction problems Universität München

11:05 – 11:40 Modeling and experimental validations Marcela Cruchaga, for free surface flow problems: collapse Universidad de

of a liquid column and sloshing cases Santiago de Chile

11:45 – 12:20 Simulation of fluid-structure interaction Kevin Wang,

problems with dynamic fracture California Institute Technology

12:25 – 1:45 Lunch

 Workshop Program

Wednesday, December 4    

Session on General Methods Chair: Christian Linder 1:45 – 2:20 Recent developments in embedded John Dolbow, Duke

interface methods University

2:25 – 3:00 A stable embedded mesh method for Mike Puso, Lawrence

computing Lagrangian and ALE finite Livermore National element methods Laboratory

3:05 – 3:40 Universal meshes: computing Ramsharan Rangarajan, triangulations conforming to planar, Brown University curved boundaries, interfaces and cracks

from background meshes 3:45 – 4:00 Break Session on Methods for Solids Chair: Charbel Farhat 4:00 – 4:35 A two-scale model for simulation Peter Wriggers, Leibniz

of problems including strong Universität Hannover discontinuities 4:40 – 5:15 Transient fluid and solid dynamics on Guglielmo Scovazzi, Duke linear tetrahedral finite elements: An University accurate and stable variational multi- scale approach 5:20 – 5:55 Multi-scale characterization and modeling Somnath Ghosh, Johns ductile failure in heterogeneous metallic Hopkins University materials 6:30 pm Bus Pick up at Stanford Guest House 7:00 – 9:00 Dinner- Trellis Restaurant Discussion on the

1077 El Camino Real day’s presentations Menlo Park, CA 94025

 Workshop Program

Thurssday, December 5    

8:20 – 8:50 Continental Breakfast available at Kavli lobby Session on General Methods Chair: Yongxing Shen 8:50 – 9:25 A dG approach to higher order ALE Ricardo Nochetto, University formulations in time of Maryland 9:30 – 10:05 High-order finite element methods for moving Adrian Lew, Stanford boundary problems with prescribed boundary University

evolution 10:10 – 10:25 Break Session on Methods for Solids Chair: Tarek Zohdi 10:25 – 11:00 Numerical treatment of discontinuities as Stephan Bilyk, Army encountered in ballistic impact events Research Laboratory 11:05 – 11:40 Universal meshes for curvilinear crack propagation Yongxing Shen, Universitat

and application to hydraulic fracturing Politècnica de Catalunya 11:45 – 12:20 Computational failure analysis for localized and Jeon-Hoon Song, University distributed failure of South Carolina 12:25 – 1:40 Lunch Session on Methods for Solids Chair: Adrian Lew 1:40 – 2:15 Phase field modeling of fracture: handling stress Alain Karma, Northeastern

singularities and crack-front geometrical University discontinuities

2:20 – 2:55 New 3D finite elements to model solids at failure Christian Linder, Stanford

University 3:00 – 3:35 Modeling and simulation of electromagnetic fabric Tarek Zohdi, University of shielding California, Berkeley

 Workshop Program

Thurssday, December 5    

3:40 – 4:00 Break Session on Reduced-Order Models Chair: Charbel Farhat 4:00 – 4:35 Real-time monitoring of thermal fields with Antonio Huerta, Universitat

parameterized domains and discontinuities Politècnica de Catalunya

4:40 – 5:15 Nonlinear reduction of embedded boundary Maciej Balajewicz, computational fluid dynamics Stanford University 5:20 – 6:00 Discussion 6:30 pm Bus pick-up at Kavli 7:00 – 9:00 Dinner - Café del Sol Restaurant Closing remarks and 1010 Doyle Street feedback Menlo Park, CA 94025 Charbel Farhat

 Workshop Attendees

     

Participant Institution Email Maciej Balajewicz Stanford University maciej.balajewicz@stanford.edu Stephan Bilyk Army Research Laboratory stephan.r.bilyk.civ@mail.mil Joshua Crone Army Research Laboratory

Marcela Cruchaga Universidad de Santiago de Chile marcela.cruchaga@usach.cl John Dolbow Duke University jdolbow@duke.edu

Charbel Farhat Stanford University cfarhat@stanford.edu

Somnath Ghosh John Hopkins sghosh20@jhu.edu Wayne Hodo Engineer Research and Development Center Antonio Huerta Universitat Politècnica de Catalunya antonio.huerta@upc.edu Sergio Idelsohn Universitat Politècnica de Catalunya sergio@cimne.upc.edu Alain Karma Northeastern University a.karma@neu.edu Adrian Lew Stanford University lewa@stanford.edu Christian Linder Stanford University linder@stanford.edu Raju Namburu Army Research Laboratories raju.namburu@us.army.mil Ricardo Nochetto University of Maryland rhn@math.umd.edu John Pellegrino Army Research Laboratories john.m.pellegrino.civ@mail.mil Mike Puso Lawrence Livermore National Laboratories puso@llnl.gov Ramsharan Rangarajan Brown University Ramsharan_Rangarajan@brown.edu Guglielmo Scovazzi Duke University guglielmo.scovazzi@duke.edu Mikhail Shashkov Los Alamos National Laboratories shashkov@lanl.gov Yongxing Shen Universitat Politècnica de Catalunya yongxing.shen@upc.edu Robert Sheroke Army Research Laboratory Robert.m.sheroke.civ@mail.mil Jeong-Hoon Song University of South Carolina jhsong@cec.sc.edu Rama Valiseppy Army Research Laboratory ramavaliseppy@yahoo.com Wolfgang Wall Technische Universität München wall@lnm.mw.tum.de Kevin Wang California Institute of Technology kevinwgy@caltech.edu  Peter Wriggers Leibniz Universität Hannover wriggers@ikm.uni-hannover.de  Tarek Zohdi University of California, Berkeley zohdi@berkeley.edu    

                 

Lagrangian Frames: an efficient and accurate way to solve multi-fluids flows Sergio Idelsohn1,2,3, Eugenio Oñate1 , Norberto Nigro3, Julio Marti1, Pablo Becker1, Juan Gimenez3

1 International Center for Numerical Methods in Engineering (CIMNE) Gran Capitan s/n, Edif. C1, Campus Nord UPC, 08034 Barcelona, Spain 2 Institució Catalana de Recerca i Estudis Avançats (ICREA) Passeig Lluís Companys 23, 08010 Barcelona, Spain 3 Centro de Investigación de Métodos Computacionales (CIMEC) Güemes 3450, S3000GLN, Santa Fe, Argentine

Abstract Many of the previous works for solving the incompressible Navier-Stokes equations have been thought for homogeneous fluids. For multi-fluids flows there are two main differences: the possibility to have evolving discontinuities on the pressure field or to have evolving discontinuities on the pressure gradients. The first case appears when there are surface tensions at the internal interfaces, or there is an internal jump in the viscosity. The second case is typical of problems with internal jumps in the density. The use of evolving discontinuous pressure or pressure gradient fields is fundamental to achieve acceptable results in multi-fluid fluid flows. In this workshop a new generation of the Particle Finite Element Method[1] (PFEM) will be developed and applied for solving the incompressible Navier-Stokes equations for heterogeneous fluid flows. In a previous version of PFEM, the authors showed the ability of Lagrangian frames to deal with problems ranging from simple fluids with a single interface to fluid mixtures with multiple interfaces [2]. Now, we will introduce a new strategy, named “X-IVAS”, that allows us to solve the same problems in a very efficient way concerning computer time. In fact, in all the cases tested, the computer times were smaller than for similar problems solved with classical Eulerian frames. This new strategy may be seen as a different way of linearizing the N-S equations that allows large time-steps with an excellent convergence rate. This particular linearization of the non-linear N-S equations exists only if the equations are written in a Lagrangian frame. In fact, in all the examples tested, only one iteration of the non-linear N-S equations was enough to achieve an excellent result. This conclusion opens a new perspective for the Lagrangian formulation of the N-S equations. To our knowledge, nowadays PFEM is the fastest algorithm for solving multi-fluid flows with nonstructured meshes. References [1] S.R. Idelsohn, E. Oñate, F. Del Pin, The particle finite element method a powerful tool to solve incompressible flows with free-surfaces and breaking waves, International Journal for Numerical Methods in Engineering 61 (2004) 964-89 [2] S.R. Idelsohn, M. Mier-Torrecilla, E. Oñate, Multi-fluid flows with the Particle Finite Element Method, Computer Methods in Applied Mechanics and Engineering 198 (2009) 2750-2767

                 

ReALE Reconnection-based Arbitrary Lagrangian Eulerian Method for Multimaterial Hydrodynamics Mikhail Shashkov

XCP-4 Group, Methods and ALgorithm, X-Computational Physics Division Los Alamos National Laboratory, Los Alamos, NM, USA (shashkov@lanl.gov)

Abstract We present a relatively new reconnection-based multi-material Arbitrary Lagrangian Eulerian (ALE) method [1, 2, 3]. The main elements in an standard ALE simulation are an explicit Lagrangian phase in which the solution and grid are updated, a rezoning phase in which a new grid is defined, and a remapping phase in which the Lagrangian solution is transferred (conservatively interpolated) onto the new grid. In standard ALE methods the new mesh from the rezone phase is obtained by moving grid nodes without changing connectivity of the mesh. Such rezone strategy has its limitation due to the fixed topology of the mesh. In our new method we allow connectivity of the mesh to change in rezone phase, which leads to general polygonal mesh and allows to follow Lagrangian features of the mesh much better than for standard ALE methods. Rezone strategy with reconnection is based on using Voronoi tessellation. Mesh smoothing is achieved by using notion of centroidal Voronoi diagrams. Because of reconnection we have to use discretizations of Lagrangian hydro, which are capable to deal with general polygonal mesh. In this work we use both cellcentered and staggered discretizations on general polygonal meshes. For remapping stage we use algorithms based on intersections of Lagrangian and rezoned mesh. We also address problems related to modeling multimaterial flows using ReALE approach. That we will briefly describe modern moment-of-fluid interface reconstruction method [4, 5] and and new interface-aware closure model for multimaterial cells [6]. We demonstrate performance of our new method on series of numerical examples and show it superiority and robustness in comparison with standard ALE methods without reconnection. In Fig. 1 we present result of application of ReALE method for Kelvin-Helmholtz instability. References [1] R. Loubere, P.H. Maire, M. Shashkov, J. Breil and S. Galera, “ReALE: A Reconnection-based Arbitrary Lagrangian-Eulerian Method”, J. Comp. Phys., 229, 4724-4761 (2010). [2] R. Loubere, P.H. Maire and M. Shashkov, “ReALE: A Reconnection-based Arbitrary Lagrangian-Eulerian Method in cylindrical geometry”, Computers & Fluids, 46 (1), 59-69 (2011). [3] Th. Harribey, J. Breil1, P.-H. Maire, M. Shashkov3, “A swept-intersection-based remapping method in a ReALE framework”, Inernational Journal for Numerical Methods in Fluids, Volume 72, Issue 6, pages

                 

697708, (2013). [4] V. Dyadechko and M. Shashkov, “Reconstruction of multi-material interfaces from moment data” Journal of Computational Physics Volume 227 Issue 11, Pages 5361-5384 (2008) [5] H.-T. Ahn and M. Shashkov, “Multi-material interface reconstruction on generalized polyhedral meshes” Journal of Computational Physics Volume 226 Issue 2, Pages 2096-2132 (2007)

Figure 1: Multimaterial Kelvin-Helmholtz Instability - Computational Mesh and Interfaces

[6] A. Barlow, R.N. Hill and M. Shashkov, “Constrained optimization framework for interface-aware subscale dynamics closure models for multimaterial cells in Lagrangian and arbitrary Lagrangian-Eulerian hydrodynamics ”, Los Alamos National Laboratory Report LAUR-13-26180, (2013). Acknowledgments This work was performed under the auspices of the National Nuclear Security Administration of the US Department of Energy at Los Alamos National Laboratory under Contract No. DE-AC52-06NA25396 and supported by the DOE Advanced Simulation and Computing (ASC) program. The last author acknowledges the partial support of the DOE Office of Science ASCR Program. LANL Report - LA-UR-13-28200. This is joint work with E. Loubere, P.-H. Maire, J. Breil, S. Galera, Th. Harribey and W. Bo.

                 

Fiver: a higher-order embedded boundary method for multi-material compressible flow and flow-structure interaction problems

Charbel Farhat, Alex Main and Vinod Lakshminarayan

Department of Aeronautics and Astronautics Department of Mechanical Engineering Institute for Computational and Mathematical Engineering Stanford University, USA

Abstract FIVER is a robust finite volume method for the solution of high-speed compressible flows in highly nonlinear multi-material domains involving arbitrary equations of state and large density jumps. The global domain of interest can include a moving or deformable solid subdomain that furthermore may undergo topological changes due to, for example, crack propagation. The key components of FIVER, include: (1) the definition of a discrete surrogate material interface, (2) the computation first of a reliable inviscid approximation of the fluid state vector on each side of a discrete material interface via the construction and solution of a local, exact, two-phase Riemann problem, (3) the algebraic solution of this auxiliary problem when the equation of state allows it, (4) the solution of this two-phase Riemann problem using sparse grid tabulations otherwise, (5) a ghost fluid scheme for approximating next the diffusive and source terms, (6) a systematic procedure for populating the ghost or inactive fluid grid points that guarantees under specified conditions the desired order of spatial accuracy, and (7) an energy conserving algorithm for enforcing the equilibrium transmission condition at a fluid-structure interface and therefore properly communicating with a finite element structural analyzer. All of the aforementioned FIVER components accommodate both explicit and implicit time-integration schemes. After motivating and reviewing FIVER, this talk will focus on demonstrating its potential for the solution of large-scale, realistic multi-phase fluid and fluid-structure interaction problems with the massively parallel simulation of the underwater implosion of an aluminum cylinder, the underbody blast of a generic hull vehicle and that of TARDEC’s ARES system, the flapping of a real pair of wings made of mylar for the generation of thrust and lift, and the pull-up and roll maneuvers of a complete, flexible, aircraft configuration. The first three applications are characterized by ultrahigh compressions, shock waves, large density jumps at the fluid material interfaces, self-contact, and the initiation and propagation of cracks in the structure. The fourth application is characterized by a turbulent viscous flow past highly flexible wings undergoing large displacements, rotations, and deformations. The last application features fluid-structure-control coupling. The lecture will also discuss correlations with experimental data, and CPU performance issues on multi-core systems.

                 

An embedded boundary method designed for complex fluid-structure interaction problems Wolfgang A. Wall, Benedikt Schott, Shadan Shahmiri, Sudhakar Yogaraj

Institute for Computational Mechanics, Technische Universität München Boltzmannstrasse 15, 85748 Garching, Germany, wall@lnm.mw.tum.de

Abstract Over the last decades, the development and application of fluid-structure interaction (FSI) simulations has gained great attention. Whereas classical ALE-based FSI approaches are limited when the structure undergoes too large displacements and/or rotations or even topological changes, fixed-grid methods able to deal with embedded boundaries represent very promising approaches with a number of attractive properties. Such embedded boundary methods are also very promising (and we have also used them) for other evolving domain flow problems, like two-phase flows or combustion. Describing the entire fluid domain by a fixed-grid Eulerian formulation using embedded boundaries allows for large and complex changes of the physical fluid domains without fluid mesh distortion or even remeshing. For the robustness and the predictive applicability for realistic and complex problems it is however essential to satisfy highest demands on approximation quality, stability and accuracy of the fixed-grid formulation, particularly with regard to the moving boundaries or interfaces in time. And most existing approaches show severe weaknesses in one or all of these aspects. In this talk we discuss a novel robust fixed-grid FSI approach for the 3D incompressible Navier-Stokes equations on moving fluid domains. The embedded boundaries are handled in a Partition of Unity or XFEM type manner. A combination of special stabilization techniques are used and extended to obtain a robust, stable and accurate fluid formulation together with an improvement of the system conditioning without element manipulation or blocking strategies for degrees of freedom. In the talk we will not only present the methods and its application to various numerical examples but we will also shed some light on the mathematical analysis. We will also show that our approach is capable of nicely handling cases with changing topologies, like in fluid-structure-contact interaction or when cracks appear at wet surfaces. Many problems need special boundary layer meshes to obtain reliable simulation results. The inability of most fixed-grid methods to handle or provide such meshes is one of the main shortcomings when targeting complex real world problems. To overcome this shortcoming we propose a hybrid ALE/fixedgrid method that is capable of dealing with deforming fluid domains (e.g. boundary layer meshes) attached to the structure in combination with a fixed background grid in an efficient and accurate way. The generality of both the design and the implementation of above-mentioned techniques allow a rather easy transfer to this hybrid case. In the final part of the talk both the hybrid method and its application to some numerical examples will be shown.

                 

Modeling and experimental validation for free surface flow problems: Collapse of a liquid column and sloshing cases Marcela A. Cruchaga

Departamento de Ingeniería Mecánica. Universidad de Santiago de Chile – USACH, Av. Bdo. O’Higgins 3363, Santiago, Chile, marcela.cruchaga@usach.cl

Abstract The present work reports an experimental validation for free surface flows formulations. In particular, the breaking dam and the sloshing problem in rectangular tanks are analyzed. The numerical study is performed using a fixed-mesh Navier-Stokes monolithic formulation coupled with two different techniques to describe the free surface evolution: a capturing [1] and a Lagrangian tracking [2] techniques. A shared memory parallel technique was implemented to compute the matrices and right hand side blocks using the Open Multiprocessing standard (OpenMP) and to solve the resulting algebraic system of equations with the Intel Math Kernel Library (MKL). Different free surface flow problems: the collapse of a liquid column [1] and sloshing cases [2] are presented. The computed results of the free surface wave history at different control points are validated with those registered from experiments. Acknowledgments The support provided by the Chilean Council for Research and Technology CONICYT (FONDECYT Project No. 1130278) and Army High Performance Computing Research Center (AHPCRC), are gratefully acknowledged. References: [1] Cruchaga, M. A., Celentano, D. J., & Tezduyar, T. E. (2009). Computational modeling of the collapse of a liquid column over an obstacle and experimental validation. Journal of applied mechanics, 76(2). [2] Marcela A. Cruchaga, Ricardo S. Reinoso, Mario A. Storti, Diego J. Celentano and Tayfun E. Tezduyar “Finite element computation and experimental validation of sloshing in rectangular tanks”. Computational Mechanics. Aceptado, 2013.

                 

Numerical Simulation of Fluid-Structure Interaction Problems with Dynamic Fracture Kevin G. Wang1, Patrick Lea2, and Charbel Farhat3

1 Department of Aerospace (GALCIT), California Institute of Technology 2 Department of Mechanical Engineering, Northwestern University 3 Department of Aeronautics and Astronautics, Department of Mechanical Engineering, and Institute for Computational and Mathematical Engineering, Stanford University

Abstract The implosive collapse and subsequent fracture of gas-filled underwater structures highlights a challenging multi-phase fluid-structure interaction problem. It is characterized by ultrahigh compressions, shock waves, large structural deformations, self-contact, and the initiation and propagation of cracks in the structure. This problem is a major area of concern in many underwater engineering applications. It is also relevant to other problems including pipeline failure driven by explosion and the comminution of kidney stone by extracorporeally generated shock waves (shockwave lithotripsy). The development of a computational approach for this problem is a formidable challenge. It requires not only incorporating in the computations material failure models, but also accounting for all possible interactions between the nonlinear structure and the external and internal fluids. In this talk, we present a high-fidelity computational framework for FSI problems involving strong shocks, multi-material fluid flows, large structural deformations, and fluid-induced crack propagation. It is based on: (1) a finite volume compressible fluid solver based on exact two-fluid and fluid-structure Riemann problems (FIVER); (2) an extended finite element method (XFEM) for nonlinear structures possibly with strong discontinuities such as cracking; (3) robust and efficient algorithms for tracking the fluid-structure interface with respect to the fixed, non body-fitted fluid mesh; (4) conservative algorithms for transferring fluid-induced loads onto the wetted surface of the structure; and (5) second-order accurate, staggered yet numerically stable time-integrators for time advancing the fluid-structure coupled system. The salient features of this computational framework will be highlighted in the full-scale simulations of several implosion and explosion experiments.

                 

Recent developments in embedded interface methods John E. Dolbow

Yoh Family Professor of Engineering Duke University

Abstract This seminar will present recent advances in an emerging class of embedded finite element methods for evolving interface problems in mechanics. By embedded, we refer to methods that allow for the interface geometry to be arbitrarily located with respect to the finite element mesh. This relaxation between mesh and geometry obviates the need for remeshing strategies in many cases and greatly facilitates adaptivity in others. The approach shares features with finite-difference methods for embedded boundaries, but within a variational setting that facilitates error and stability analysis. We focus attention on a weighted form of Nitsche's method that allows interfacial conditions to be robustly enforced. Classically, Nitsche's method provides a means to weakly impose boundary conditions for Galerkin-based formulations. With regard to embedded interface problems, some care is needed to ensure that the method remains well behaved in varied settings ranging from interfacial configurations resulting in arbitrarily small elements to problems exhibiting large contrast. We illustrate how the weighting of the interfacial terms can be selected to both guarantee stability and to guard against ill-conditioning. We then present results from various benchmark problems in frictional contact, including situations involving triple junctions.

                 

A Stable Embedded Mesh Method for Coupling Lagrangian and ALE Finite Element Models M. Puso, E. Kokko, B. Liu, B. Simpkins

Lawrence Livermore National Laboratory (puso@llnl.gov, kokko1@llnl.gov, liu15@llnl.gov, simpkins2@llnl.gov)

Abstract An embedded mesh method for coupling foreground Lagrange meshes with background multiple material ALE finite-element meshes [1] is presented. A Lagrange multiplier approach is used to enforce velocity constraints at the interface. Modifications are made to the advection scheme to account for the background fluid flow around the Lagrange body. The schemes for computing the Lagrange multipliers and time integrating the explicit equations of motion were designed to be provably stable. Details of the stability analysis will be presented. It is also shown that the method has no deleterious affect on the stable Courant time steps i.e. there is no modification of the time step to account for the embedded mesh. Consequently, the proposed approach exhibits excellent robustness in a variety of rigorous analyses. Mesh studies are presented demonstrating convergence. Example problems including contact, penetration, blast and failure with evolving fragmentation (Fig. 1) are also presented.

Figure 1. Pipe bomb with steel Lagrangian foreground mesh and air mixed with explosive in background. (a) Lagrange mesh fails at high pressure and erodes forcing gas (red) between pipe fragments (blue). (b) Velocity plot shows high rate of pluming gas and slower steel fragments. References [1] M. Puso, J. Sanders, R. Settgast, and B. Liu “An Embedded Mesh Method in a Multiple Material ALE”, Computer Methods in Applied Mechanics and Engineering (15) 245-246, pp.273-289, 2012. Work performed under the HPC Software Application Institute on Blast Protection for Platforms and Personnel under funding from the DoD HPC Modernization Program

                 

Universal Meshes: Computing triangulations conforming to planar, curved boundaries, interfaces and cracks from background meshes Ramsharan Rangarajan1 & Adrian Lew2

1School of Engineering, Brown University. 2Department of Mechanical Engineering, Stanford University. email: rram@brown.edu, lewa@stanford.edu

Abstract A large class of computational methods for problems with evolving domains and discontinuities require robust and automatic methods to discretize the changing geometry. We introduce a method to create triangulations that conform to curved domain boundaries, interfaces and cracks by transforming a small collection of triangles in a background mesh. In the process, no new vertices are introduced and connectivities of triangles are left unaltered. The method can render both straight-edged and curvilinear triangulations that conform to an immersed boundary/interface/crack with desired accuracy, even exactly. The method serves as a quick and simple tool for \meshing" domains with complex boundaries, interfaces and cracks. It provides significant algorithmic advantages for simulating problems with evolving domains and in numerical schemes that require iterating over the geometry of domains. With no conformity requirements, the same background mesh, called a universal mesh, can be adopted to triangulate a large family of domains immersed in it, including ones realized over several updates during the coarse of simulating problems with moving boundaries. High-order finite elements constructed over curved triangles computed by the method achieve optimal accuracy, which has customarily proven difficult in numerical schemes that adopt nonconforming meshes. At the workshop, we will present the details of the method, discuss results guaranteeing its robustness, and demonstrate its performance with numerous examples. We will also discuss some open questions and mention encouraging results in three-dimensions.

                 

A two-scale model for simulation of problems including strong discontinuities P. Wriggers

Leibniz Universität Hannover Abstract A concurrent two-scale and two-method approach for modeling of problems including discontinuities is presented. The applications relate to dry frictional noncohesive granular materials. In domains that include finite and discontinuous deformation the material is modeled at the grain scale using a three-dimensional discrete element method. In the remaining domain the material is considered continuous and modeled by the finite element method using an elasto–plastic constitutive equation. The parameters of this contstitutive equation is fit to the particle model via a homogenization scheme in order to have a continuous description of the material behaviour across the scales. The discrete and finite element models are coupled at the interface by the Arlequin method. An overlapping domain is introduced where the overall virtual work is interpolated between both models and compatibility is ensured by kinematic constraints. For this purpose the displacements of the discrete particles are split into a fine and coarse scale part and equality of the coarse scale part and the continuum solution is enforced through a penalty formulation. Examples show the applicability of the scheme to real world problems.

                 

Transient fluid and solid dynamics on linear tetrahedral finite elements: An accurate and stable variational multi-scale approach Guglielmo Scovazzi

Department of Civil and Environmental Engineering, Duke University (guglielmo.scovazzi@duke.edu)

Abstract A new tetrahedral finite element for transient dynamic computations of fluids [1] and solids [2] is presented. It utilizes the simplest possible finite element interpolations: Piece-wise linear continuous functions are used for displacements and pressures (P1/P1), while the deviatoric part of the stress tensor (if present, as in the case of solids) is evaluated with simple single-point quadrature formulas. The variational multiscale stabilization eliminates the pressure checkerboard instabilities affecting the numerical solution in the case of the Darcy-type operator related to compressible fluids computations, or the Stokes-type operator related to solid dynamics computations. The formulation is extended to strong shock computations in fluids and to elastic-plastic flow in solids (see Fig. 1). Extensive tests of shock flows in fluids, and of linear elasticity and finite elastoplasticity (compressible as well as nearly incompressible) will be presented. Because of its simplicity, the proposed element could favorably impact complex geometry, fluid/structure interaction, and embedded discontinuity computations. Time permitting, a number of preliminary results on fluid-structure interaction problems will also be presented.

Figure 1: High velocity impact, elastic-plastic finite strain computation using the proposed approach. References [1] G. Scovazzi, “Lagrangian shock hydrodynamics on tetrahedral meshes: A stable and accurate variational multiscale approach”, J. Comp. Phys., 231(24), pp. 8029-8069, 2012. [2] G. Scovazzi and B. Carnes, “Accurate and stable transient solid dynamics computations on linear finite elements: A variational multiscale approach”, Int. J. Num. Meth. Engr., (in preparation), 2013. This work was supported by Sandia National Laboratories under various grants, among which the Computer Science Research Foundations (2010-2013) and Laboratory Directed Research & Development (2013-2015) programs.

                 

Multi-Scale Characterization and Modeling of Ductile Failure in Heterogeneous Metallic Materials Somnath Ghosh

Departments of Civil Engineering and Mechanical Engineering Johns Hopkins University, Baltimore, MD 21218, E-mail: sghosh20@jhu.edu

Abstract Many metals and alloys, e.g. cast aluminum alloys contain microstructural heterogeneities in form of silicon particulates, intermetallics, precipitates and voids. Experimental studies on ductile failure in have shown that these morphological variations strongly affect microstructural damage nucleation due to particulate cracking and interfacial decohesion, as well as ductile damage growth by matrix rupture due to void growth and coalescence. Modeling these materials requires consideration of large domains with special attention on the microstructural morphology. The concept of multi-scale modeling provides the necessary framework for selective micro-analysis in a very limited region of a macroscopic computational domain. The multiscale models undergo domain partitioning based on the evolution of stresses, strains and/or damage in the microstructure. This presentation will discuss four important ingredients of multi-scale modeling of ductile failure in heterogeneous cast aluminum alloys. These include: (i) a multi-scale characterization based preprocessor for multi-scale models; (ii) microstructural analysis module for ductile fracture; (iii) a homogenization based continuum damage model for ductile materials that can be used in macroscopic analysis modules and (iv) a multi-scale framework for ductile crack propagation. In a concurrent multi-scale model, it is prudent to partition the initial computational domain based on information of the underlying microstructure, prior to mechanical analysis. The morphology-based domain partitioning (MDP), as a preprocessor to multiscale modeling, is intended for two reasons: (1) to determine microstructural RVE's that can be used in the "bottom-up" homogenization for different regions in the computational domain; and (2) to identify those regions, where the morphology alone can cause a breakdown in the homogenization assumption. For effective micro-mechanical modeling, the Voronoi Cell FEM model will be discussed. The model will account for particle fragmentation in the microstructure and ductile failure through matrix cracking in the form of void growth and coalescence. An adaptive, locally enriched VCFEM or LE-VCFEM framework is developed for simulating ductile fracture in narrow bands of localized plastic flow and void growth. An anisotropic continuum damage model for pressure dependent plastic materials is developed for macroscopic analysis in a multi-scale material modeling framework. The model is based on homogenization of microstructural variables obtained by LE-VCFEM analysis of microstructural representative volume element (RVE) containing particles, matrix and voids. Finally, all of the above modules will be integrated in an adaptive concurrent multi-scale framework to model the entire evolution of a ductile crack.

                 

A dG approach to higher order ALE formulations in time Ricardo H. Nochetto University of Maryland Abstract We present recent results on time-discrete discontinuous Galerkin (dG) methods for advection-diffusion model problems defined on deformable domains and written on the Arbitrary Lagrangian Eulerian (ALE) framework. ALE formulations deal with PDEs on deformable domains upon extending the domain velocity from the boundary into the bulk with the purpose of keeping mesh regularity. We describe the construction of higher order in time numerical schemes enjoying stability properties independent of the arbitrary extension chosen. Our approach is based on the validity of Reynolds' identity for dG methods which generalize to higher order schemes the Geometric Conservation Law (GCL) condition. We briefly discuss stability, a priori and a posteriori error analyses and illustrate them by insightful numerical experiments. This is joint work with A. Bonito and I. Kyza.

                 

High-Order Finite Element Methods for Moving Boundary Problems with Prescribed Boundary Evolution Adrian Lew

Stanford University (lewa@stanford.edu)

Abstract We develop a framework for the design of finite element methods for moving boundary problems with prescribed boundary evolution that have arbitrarily high order of accuracy, both in space and in time. At the core of our approach is the use of a universal mesh: a stationary background mesh containing the domain of interest for all times that adapts to the geometry of the immersed domain by adjusting a small number of mesh elements in the neighborhood of the moving boundary. The resulting method maintains an exact representation of the (prescribed) moving boundary at the discrete level, yet is immune to large distortions of the mesh under large deformations of the domain. The framework is general, allowing one to achieve any desired order of accuracy in space and time by selecting a suitable finite-element space on the universal mesh and a suitable time integrator for ordinary differential equations. In the process of deriving our method, we present a unified, geometric framework that puts our method and conventional deforming-mesh methods on a common footing suitable for analysis. The main idea is to recast the governing equations on a sequence of cylindrical spacetime slabs that span short intervals of time. The clarity brought about by this geometric viewpoint renders the analysis of numerical methods for moving-boundary problems more tractable, as it reduces the task to a standard analysis of fixed-domain problems with time-dependent PDE coefficients. Using the analytical framework so described, we prove a general error estimate for a class of finite-element methods for moving boundary problems that includes our universal-meshing method and existing deforming-mesh methods as special cases. We verify the aforementioned error estimates with several numerical examples in one and two dimensions.

                 

Numerical Treatment of Discontinuities as Encountered in Ballistic Impact Events S. Bilyk and R. Becker

Army Research Laboratory Aberdeen Proving Ground, MD 21005-5066

Abstract In the past decade several computational techniques have been developed to ease difficulties for solving problems with localized features that are not efficiently resolved by mesh refinement. Several of these have been implemented and/or currently being developed in large-scale parallel platform multi-physics hydrocodes used by the Army for material response under extreme environments (for e.g. high strains, strain rates, pressures, temperatures, EM fields, etc.). One of the initial applications was the modeling of new surfaces arising from material failure. In addition to the numerical representation of evolving interfaces, challenges remain in transitioning fracture mechanisms to efficient continuum applications. Much has been learned, and numerous models incorporating lower length scale mechanisms have been proposed and demonstrated. Yet, for numerous reasons, few of these micromechanical models have found common use. Often the problem is not in understanding the physics but rather in creating a robust and efficient mathematical formulation and numerical implementation—a manifestation of the scale bridging problem. This presentation will examine several micromechanical mechanisms contributing to fracture where the underlying physics are reasonably well understood and can be modeled, but the transition to more comprehensive, robust and efficient algorithms in large scale continuum codes remains elusive. Complications surrounding modeling of strain localization and macroscale fracture for multi-material systems subjected to strong shock waves and high deformations will be described, and recent DOE hydrocode development activities in XFEM and embedded grids relevant for Army protection applications will be presented. Future challenges will be identified.

                 

Universal meshes for curvilinear crack propagation and application to hydraulic fracturing Michael J. Hunsweck1, Ramsharan Rangarajan2, Yongxing Shen3, Adrian J. Lew4

1Intel Corporation (mhunsweck@alumni.stanford.edu) 2School of Engineering, Brown University (Ramsharan Rangarajan@brown.edu) 3Laboratori de C`alcul Num`eric, Universitat Polit`ecnica de Catalunya (UPC BarcelonaTech) (yongxing.shen@upc.edu) 4Department of Mechanical Engineering, Stanford University (lewa@stanford.edu)

Abstract A critical challenge in computational fracture mechanics with the finite element method is the need to continuously update the mesh for domains with propagating cracks. In this presentation we address this question with a new algorithm for simulating the quasi-static growth of curvilinear cracks in planar domains. The main idea consists in perturbing vertices of a given background triangulation to conform it to an embedded crack. In principle, it is possible to perturb the same background mesh as the crack evolves; we call such a background mesh a universal mesh for the crack. Such perturbations to the vertices of the universal mesh are restricted to a small neighborhood of the crack. In other words, most triangles in the universal mesh are not altered. Perhaps more significantly, no vertices are added or deleted and the connectivities of triangles in the mesh are maintained. As a result, the sparsity of data structures (stiffness matrix) remains the same as the crack propagates, except for changes resulting from the duplication of displacement degrees of freedom along the crack and from the possible addition and removal of enrichments. We demonstrate the performance of the meshing algorithm and the numerical scheme for curvilinear crack propagation with examples in linear elastic fracture mechanics (LEFM) and hydraulic fracturing.

                 

Computational Failure Analysis for Localized and Distributed Failure Jeong-Hoon Song

Department of Civil and Environmental Engineering, University of South Carolina (jhsong@cec.sc.edu)

Abstract The modeling of discontinuities that are independent of the mesh is a very useful capability in fracture analysis with finite elements. A conventional finite element method for modeling discontinuities is to make them coincident with element edges and to then introduce an additional set of nodes so that the functions can be discontinuous across the finite element edges. However, such methods are quite unwieldy for evolving discontinuities, such as growing cracks. In this presentation, we will present two variants of the extended finite element method (XFEM) that can allow us to model evolving strong discontinuity without mesh dependencies: The phantom node method [1]: in this method, the intra-element discontinuity is described by a set of phantom nodes and two superimposed element layers. The formalism is somewhat different from that of the conventional XFEM approach, but the basis functions in this method are identical to the XFEM. Moreover, the proposed method simplifies the treatment of elements that are cracked since it can be implemented as two elements with modified areas. The cracking node method [2]: the method is based on introducing discontinuities only at the finite element nodes based on the XFEM approach. Thus the discontinuity in the model dose not form a continuous path, but instead a set of disconnected discontinuities. By limiting the discontinuities to nodes, the placement and the sharpness of the discontinuity representation is diminished somewhat, but we can circumvent the difficulties arising from the tracking of complicated crack paths. References [1] J.H. Song, P.M.A. Areias and T. Belytschko, “A method for dynamic crack and shear band propagation with phantom nodes”, International Journal for Numerical Methods in Engineering, 67, pp. 868–893, 2006. [2] J.H. Song and T. Belytschko “Cracking node method for dynamic fracture with finite elements”, Inter- national Journal for Numerical Methods in Engineering, 77, pp. 360–385, 2009. This work performed under the support of the Office of Naval Research under Grants N00014-13-1-0386.

                 

Phase Field Modeling of Fracture: Handling Stress Singularities and Crack-Front Geometrical Discontinuities Alain Karma 1, Matteo Nicoli 1, and Antonio Pons 2

1 Department of Physics and Center for Interdisciplinary Research on Complex Systems, Northeastern University, Boston, Massachusetts 02115, USA (a.karma@neu.edu, nmatteo.math@gmail.com) 2 Department of Physics and Nuclear Engineering, Polytechnic University of Catalonia, Terrassa, Barcelona 08222, Spain (a.pons@upc.edu)

Abstract The phase-field method has emerged as a powerful method to simulate crack propagation [1]. This method automatically regularizes stress singularities by introducing a smoothly varying scalar field _ that distinguishes between “intact” and “broken” phases of the material [2] and can also be interpreted as a phenomenological measure of damage. The phase field model is formulated as coupled dynamical equations for the phase and displacement fields that are derived variationally from an energy functional with both elastic strain and surface energy contributions. The phase field equations incorporate both the short scale physics of materials failure and macroscopic elasticity. Moreover, those equations can be related to the classical framework of linear elastic fracture mechanics (LEFM) through an asymptotic analysis of the phase field equations [3]. In addition, those equations scan be simulated on massively parallel computer architecture to describe geometrically complex dynamical phenomena such as crack nucleation, crack kinking and branching, and crack-front segmentation in three dimensions. This talk will illustrate the ability of the phase field approach to simulate geometrically complex and discontinuous fracture paths in mixed mode I+III loading [4] and how the results have inspired new analyses in the LEFM framework [5].

Figure 1: Example of phase field simulations of crack propagation. Left: displacement field during oscillatory fracture in pure antiplane shear mode III loading. Right: crack front segmentation in fully three dimensional mixed mode I+III fracture. The advancing crack front is showed at different times with time increasing from top to bottom. The top frame shows the initial helical instability of the parent crack that evolves nonlinearly into an array of fully segemented daugther cracks in the bottom frame. [4].

                 

References [1] R. Spatscheck, E. Brener, and A. Karma, Phase-Field Modeling of Crack Propagation, Phil. Mag. 91 75–95 (2011). [2] A. Karma, H. Levine, and D. Kessler, Phase-Field Model of Mode-III Dynamic Fracture, Phys. Rev. Lett. 87, 045501 (2001). [3] V. Hakim and A. Karma, Laws of crack motion and phase-field models of fracture, J. Mech. Phys. Solids 57, 342–368 (2009). [4] A. Pons and A. Karma, Helical crack-front instability in mixed mode fracture, Nature 464, 85-89 (2010). [5] J.-B. Leblond, A. Karma, and V. Lazarus, Theoretical analysis of crack front instability in mode I+III, J. Phys. Mech. Solids 59, 1872-1887 (2011).

                 

New 3D finite elements to model solids at failure Christian Linder

Department of Civil and Environmental Engineering, Stanford University (linder@stanford.edu)

Abstract We will present new finite elements with embedded strong discontinuities to model failure in three dimensional electromechanical coupled materials. Following the strong discontinuity approach for two dimensional mechanical [1] and electromechanical problems [2], we decompose the overall electromechanical boundary value problem into a continuous global and a discontinuous local part where strong discontinuities in the displacement field and the electric potential are introduced. Those strong discontinuities are incorporated through the introduction of nine mechanical enhanced parameters [3] and three new electrical enhanced parameters [5] within the individual finite elements, which can be statically condensed out on the element level resulting in a computationally highly efficiency formulation. The onset of failure is detected through the concept configurational forces and a smooth failure surface propagation is assured through the usage of the newly proposed marching cubes concept [4] applied to material failure simulations.

Figure 1: Three point bending test with different notch locations of an electromechanically loaded PZT-4 piezoelectric ceramic [5]. The numerical crack path agrees well with the experimentally observed front view of the failure zone. References [1] C. Linder and F. Armero, “Finite elements with embedded strong discontinuities for the modeling of failure in solids”, Int. J. Numer. Methods Engrg., 72(12), pp. 1391–1433, 2007. [2] C. Linder, D. Rosato and C. Miehe, “New finite elements with embedded strong discontinuities for the modeling of failure in electromechanical coupled solids”, Comput. Methods Appl. Mech. Engrg., 200(1-4), pp. 141–161, 2011. [3] F. Armero and J. Kim, “Three-dimensional finite elements with embedded strong discontinuities to model material failure in the infinitesimal range”, Int. J. Numer. Methods Engrg., 91(12), pp. 1291– 1330, 2012. [4] C. Linder and X. Zhang, “A marching cubes based failure surface propagation concept for 3D finite elements with non-planar embedded strong discontinuities of higher order kinematics”, Int. J. Numer. Methods Engrg., 96(6), pp. 339–372, 2013. [5] C. Linder and X. Zhang, “New 3D finite elements with embedded strong discontinuities to model failure in electromechanical coupled materials”, Comput. Methods Appl. Mech. Engrg., (submitted).

                 

Modeling and Simulation of Electromagnetic Fabric Shielding Tarek I. Zohdi

Professor, Department of Mechanical Engineering, Chair, UC Berkeley Computational Science and Engineering Program University of California, Berkeley

Abstract Recently, several applications have arisen that involve the dynamic of response of new material systems undergoing large finite deformations with evolving fissures and interfaces. In many cases, there is significant multifield coupling, which requires methods that can capture the unique and essential physics of these systems. In this presentation, I discuss the modeling and simulation of electrified structural fabric, with applications driven by ballistic fabric shielding, involving the deformation of electromagnetically-sensitive fabric via external electromagnetic fields and incoming high-speed external objects. This work investigates the deformation of electrified textiles in the presence of an externally supplied magnetic field. The electrification is delivered by running current through the fibers from an external power source. Of primary interest is to ascertain the resulting electromagnetic forces imposed on the fabric, and the subsequent deformation. As the fabric deforms, the current changes direction and magnitude, due to the fact that it flows through the fabric. The charge density is dictated by Gauss' law. In order to simulate such a system, one must solve a set of coupled equations governing the charge distribution, current flow and system dynamics. The deformation of the fabric, as well as the charge distribution and current flow, are dictated by solving the coupled system of differential equations for the motion of lumped masses, which are coupled through the fiber-segments under the action of electromagnetically-induced forces acting on a reduced order network model. In the work, reduced order models are developed for (a) Gauss' law (b) the conservation of current/charge and (c) the system dynamics. A temporally-adaptive, recursive, staggering scheme is developed to solve this strongly coupled system of equations. We also consider the effects of progressive fiber damage/rupture during the deformation process, which leads to changes (reduction) in the electrical conductivity and permittivity throughout the network. Numerical examples are given, as well as extensions to thermal effects, which are induced by the current-induced Joule-heating.

                 

Real-time monitoring of thermal fields with parameterized domains and discontinuities Antonio Huerta, A. Ammar, F. Chinesta, E. Cueto, A. Leygue, S. Zlotnik, and P. Díez Abstract The real-time evaluation of a thermal field in a parameterized domain with discontinuities is the objective of this presentation. Moreover, sensibilities, which could be used in optimization or inverse problems, can also be computed because the solution is written in terms of known functions of the parameters. Given choice of some parameters defining the problem geometry either as the exterior evolving boundary of interior discontinuities. The main objective of this work is to describe an original approach for computing an off-line parametric solution. That is, a solution able to include information for different parameter values and also allowing to compute readily the sensitivities. A reduced order model (the Proper Generalized Decomposition-PGD) [1] is used to circumvent the computational overhead of a multidimensional solution. References [1] A. Ammar, A. Huerta, F. Chinesta, E. Cueto, and A. Leygue, “Parametric solutions involving geometry: A step towards efficient shape optimization,” Computer Methods in Applied Mechanics and Engineering, Volume 268, pp. 178-193, (2014), http://dx.doi.org/10.1016/j.cma.2013.09.003

                 

Nonlinear Reduction of Embedded Boundary Computational Fluid Dynamics Maciej Balajewicz Stanford University Abstract Embedded boundary methods for CFD and fluid-structure interaction problems alleviate computational challenges associated with meshing and large wall boundary motions, deformations, and even topological changes. Developing model order reduction methods for computational frameworks based on the embedded boundary method seems however to be challenging. Indeed, most popular model reduction techniques are projection-based and rely on the computation of fluid basis functions based on simulation snapshots. In a traditional body-fitted computational framework, this computation is straightforward because the fluid always occupies the same computational domain. In the embedded computational framework however, deriving global fluid basis functions is problematic {a priori} because the Eulerian fluid mesh is occluded by the moving Lagrangian structural mesh. This prevents application of traditional snapshot matrix factorization techniques such as singular value decomposition because these techniques assume complete state observability. In this talk, we formulate the basis seeking problem as a low-rank approximation problem with missing data and summarize a computational optimization algorithm to solve it. To this effect, a model embedded-boundary CFD scheme that is representative of a large class of embedded boundary methods is developed. Then, we review an effective nonlinear model order reduction method based on a Petrov-Galerkin projection and Gauss-Newton minimization. Finally, we report on successful model reduction results for two-dimensional, vortex-dominated, viscous flows