Bulletin of the American Physical Society
16th APS Topical Conference on Shock Compression of Condensed Matter
Volume 54, Number 8
Sunday–Friday, June 28–July 3 2009; Nashville, Tennessee
Session V5: CM-6: Computational Methods |
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Chair: Sunil Dwivedi, Washington State University Room: Cheekwood GH |
Thursday, July 2, 2009 1:30PM - 1:45PM |
V5.00001: Automatic Conversion Of Distorted Hexahedral Elements Into Meshless Particles During Dynamic Deformation Charles Gerlach, Gordon Johnson This article presents an algorithm to automatically convert distorted hexahedral elements into meshless particles during dynamic deformation. Automatic conversion from tetrahedral elements to meshless particles has already been shown to be a robust approach for computing impact computations with severe distortions in a Lagrangian framework. With this approach the initial grid is composed of finite elements, and the highly-distorted elements are then automatically converted into meshless particles as the computations progress. This allows mild structural deformations to be accurately and efficiently computed with finite elements, and the highly-distorted regions to be robustly represented with meshless particles. Several contact conditions must be considered: element on element, particles attached to elements, and particles contacting and sliding on elements. Applying these contact conditions to hexahedral elements is made more challenging by some of the inherent properties of those elements, such as non-planar element faces. This article presents the hexahedral element conversion algorithm, along with the implementation of the above contact conditions. Several examples of high-velocity impacts are included to demonstrate the capabilities of the algorithm. [Preview Abstract] |
Thursday, July 2, 2009 1:45PM - 2:00PM |
V5.00002: A Generalized Finite Element Formulation for 3D Microscale Simulation of the Response of Heterogeneous Materials to Dynamic Loading Joshua Robbins, Thomas Voth Most engineering materials exhibit significant heterogeneity at the microscale due to polycrystalline and/or multi-phase structure, inclusions, voids, and micro-cracks. Much of the complex, nonlinear response observed in these materials originates at this length scale. The Generalized Finite Element Method (GFEM) greatly simplifies explicit treatment of material microstructure [1] by allowing for non-conformal discretization without loss of accuracy. We present our application of the GFEM to examine the dynamic response of polycrystalline materials at the microscale. The microstructure is approximated with a Voronoi tessellation, and the material basis of each resulting grain is selected randomly. An anisotropic single crystal constitutive model is applied in the local basis. The method has been implemented for massively parallel computation using a geometric decomposition and the Message Passing Interface (MPI) standard. [1] Simone A., Duarte C.A., Van der Giessen E., 2006, ``A generalized finite element method for polycrystals with discontinuous grain boundaries,'' Int. J. Numer. Methods Eng., 67, pp. 1122-1145. (Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.) [Preview Abstract] |
Thursday, July 2, 2009 2:00PM - 2:15PM |
V5.00003: A Three-dimensional Contact Algorithm for Sliding Surface Based on Triangular Subdivision Local Search in high pressure Yuxi Jiang, Haibing Zhou, Shudao Zhang The Lagrangian approach is the natural choice to model the interface movement of the matter in high pressure. The contact algorithm is one of the most crucial parts of the Lagrangian simulation and the local contact search which is to find for a node's contact point on the interface is the important part of the contact algorithm. The efficient local contact search algorithms were rarely achieved expect the node-to-segment algorithm, pinball algorithm and the inside-outside algorithm. These algorithms are either time consuming and unstable when the mesh is severely distorted or not always suitable for applications involving high explosives. Within our computational group at IAPCM, the shock compressed dynamical problems are modeled using CHAP3D code developed upon the compatible Lagrangian numerical methods. In the contact algorithm in CHAP3D code, a triangular subdivision local contact search algorithm has been developed. A shape heart is introduced by averaging the positions of the four contact segment nodes in this method. Then a four-node quadrilateral contact surface segment may be subdivided into four triangular sub-segments which normal vectors are confirmed. Therefore the contact point is achieved by the geometry method. The applications of sliding explosion simulations show the efficiency and robustness of this contact algorithm. [Preview Abstract] |
Thursday, July 2, 2009 2:15PM - 2:30PM |
V5.00004: New Formulation of Artificial Viscosity for Lagrangian Analysis of Shocks Haibing Zhou, Jun Xiong, Shudao Zhang We have developed a new artificial viscosity that satisfies a set of conditions set out by Caramana. \footnote{E. J. Caramana, M. J. Shashkov and P. P. Whalen, J. Comp. Physics, 144, 70-97, 1998.} This is based on Lew’s\footnote{A. Lew, R. Radovitzky and M. Ortiz, J. Computer-Aided Materials Design, 8, 213-231, 2001.} artificial viscosity. Due to the tensor nature of the new artificial viscosity, it reduces the dependence of the numerical solution on the grid. Central to this formulation is an eigenvalue viscosity limiter to control the magnitude of the artificial viscosity. This is effected in a simple and straightforward manner to obtain forms of artificial viscosity that are able to distinguish between adiabatic and shock compression. The formulation is applicable to any number of dimensions and for grids that are either logically rectangular or unstructured. The viscous stress is simply computed with respect to a given element of grid that always yields the compression condition and with limiter functions computed with respect to neighbor element. [Preview Abstract] |
Thursday, July 2, 2009 2:30PM - 2:45PM |
V5.00005: Density Functional Theory and Finite Deformation Elastic and Thermoelastic Constitutive Relationships Zhibo Wu, Sathya Hanagud This paper addresses the problem of obtaining the complete constitutive relationships for solids under conditions of finite deformations from first principles by the use of the density functional theory, phonon thermal energy contributions, electron thermal energy contributions and foundations of continuum mechanics of finite deformation elasticity and thermoelasticity. In the work, to date, the invariance requirements concerning the crystal symmetry under specific rotations and objectivity is not addressed. This means if the deformed coordinates x $\to $QF then U(F) = U(QF) for every Q in the spatial orthogonal group. (The deformation gradient is denoted by F.) First, this implies that U= U(C) =U(F$^{T}$F) where C = F$^{T}$F is the stretch or the Cauchy-Green deformation tensor. Next, the crystal symmetry is characterized by the material or solid symmetry group G$_{M}$ . Then U(C) = U (QC) for all Q$\in $G$_{M}$ .This then requires the use of structural tensors introduced by Boehler. Thus, to satisfy the principle of objectivity the energy obtained from DFT by straining the lattice should be expressed as functions of the invariants of the stretch tensor C and the structural tensors applicable to the specific crystal symmetry group. Then, the second Piola-Kirchhoff stress tensor S = F$^{-1}$T = 2$\partial $U/$\partial $C. T is the first Piola- Kirchhoff stress tensor. For thermoelasticity the free energy is then obtained. [Preview Abstract] |
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