Interaction and multiscale mechanics

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Multiscale modeling of elasto-viscoplastic polycrystals subjected to finite deformations

  • Matous, Karel (Department of Aerospace and Mechanical Engineering, University of Notre Dame) ;
  • Maniatty, Antoinette M. (Department of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute)
  • Received : 2009.08.22
  • Accepted : 2009.11.26
  • Published : 2009.12.25
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Abstract

In the present work, the elasto-viscoplastic behavior, interactions between grains, and the texture evolution in polycrystalline materials subjected to finite deformations are modeled using a multiscale analysis procedure within a finite element framework. Computational homogenization is used to relate the grain (meso) scale to the macroscale. Specifically, a polycrystal is modeled by a material representative volume element (RVE) consisting of an aggregate of grains, and a periodic distribution of such unit cells is considered to describe material behavior locally on the macroscale. The elastic behavior is defined by a hyperelastic potential, and the viscoplastic response is modeled by a simple power law complemented by a work hardening equation. The finite element framework is based on a Lagrangian formulation, where a kinematic split of the deformation gradient into volume preserving and volumetric parts together with a three-field form of the Hu-Washizu variational principle is adopted to create a stable finite element method. Examples involving simple deformations of an aluminum alloy are modeled to predict inhomogeneous fields on the grain scale, and the macroscopic effective stress-strain curve and texture evolution are compared to those obtained using both upper and lower bound models.

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