, Volume 68, Issue 5, pp 1427–1445 | Cite as

Direct Numerical Simulations in Solid Mechanics for Quantifying the Macroscale Effects of Microstructure and Material Model-Form Error

  • Joseph E. Bishop
  • John M. Emery
  • Corbett C. Battaile
  • David J. Littlewood
  • Andrew J. Baines


Two fundamental approximations in macroscale solid-mechanics modeling are (1) the assumption of scale separation in homogenization theory and (2) the use of a macroscopic plasticity material model that represents, in a mean sense, the multitude of inelastic processes occurring at the microscale. With the goal of quantifying the errors induced by these approximations on engineering quantities of interest, we perform a set of direct numerical simulations (DNS) in which polycrystalline microstructures are embedded throughout a macroscale structure. The largest simulations model over 50,000 grains. The microstructure is idealized using a randomly close-packed Voronoi tessellation in which each polyhedral Voronoi cell represents a grain. An face centered cubic crystal-plasticity model is used to model the mechanical response of each grain. The overall grain structure is equiaxed, and each grain is randomly oriented with no overall texture. The detailed results from the DNS simulations are compared to results obtained from conventional macroscale simulations that use homogeneous isotropic plasticity models. The macroscale plasticity models are calibrated using a representative volume element of the idealized microstructure. Ultimately, we envision that DNS modeling will be used to gain new insights into the mechanics of material deformation and failure.


Direct Numerical Simulation Representative Volume Element Plasticity Model Mesh Refinement Direct Numerical Simulation Result 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



We would like to thank Ben Reedlunn for suggesting that we explore the use of the Hosford yield criteria. Also, we would like to thank Bill Scherzinger for the implementation of the Hosford plasticity algorithm within the Sierra finite-element software and discussions of its use. Sandia National Laboratories is a multi-program laboratory operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the US Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.


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Copyright information

© The Minerals, Metals & Materials Society (outside the U.S.) 2016

Authors and Affiliations

  1. 1.Engineering Sciences CenterSandia National LaboratoriesAlbuquerqueUSA
  2. 2.Materials Science and Engineering CenterSandia National LaboratoriesAlbuquerqueUSA
  3. 3.Computing Research CenterSandia National LaboratoriesAlbuquerqueUSA
  4. 4.General Motors Proving GroundGeneral MotorsMilfordUSA

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