Variational projection methods for gradient crystal plasticity using Lie algebras

Truster, Timothy J.; Nassif, Omar

doi:10.1002/nme.5355

Title: Variational projection methods for gradient crystal plasticity using Lie algebras

Journal Article · Wed Oct 19 00:00:00 EDT 2016 · International Journal for Numerical Methods in Engineering

DOI:https://doi.org/10.1002/nme.5355· OSTI ID:1401475

^[1]; Nassif, Omar ^[1]

Department of Civil and Environmental Engineering University of Tennessee, Knoxville 318 John D. Tickle Engineering Building 37921 Knoxville TN USA

Summary A computational method is developed for evaluating the plastic strain gradient hardening term within a crystal plasticity formulation. While such gradient terms reproduce the size effects exhibited in experiments, incorporating derivatives of the plastic strain yields a nonlocal constitutive model. Rather than applying mixed methods, we propose an alternative method whereby the plastic deformation gradient is variationally projected from the elemental integration points onto a smoothed nodal field. Crucially, the projection utilizes the mapping between Lie groups and algebras in order to preserve essential physical properties, such as orthogonality of the plastic rotation tensor. Following the projection, the plastic strain field is directly differentiated to yield the Nye tensor. Additionally, an augmentation scheme is introduced within the global Newton iteration loop such that the computed Nye tensor field is fed back into the stress update procedure. Effectively, this method results in a fully implicit evolution of the constitutive model within a traditional displacement‐based formulation. An elemental projection method with explicit time integration of the plastic rotation tensor is compared as a reference. A series of numerical tests are performed for several element types in order to assess the robustness of the method, with emphasis placed upon polycrystalline domains and multi‐axis loading. Copyright © 2016 John Wiley & Sons, Ltd.

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Sponsoring Organization:: USDOE

OSTI ID:: 1401475

Journal Information:: International Journal for Numerical Methods in Engineering, Journal Name: International Journal for Numerical Methods in Engineering Vol. 110 Journal Issue: 4; ISSN 0029-5981

Publisher:: Wiley Blackwell (John Wiley & Sons)Copyright Statement

Country of Publication:: United Kingdom

Language:: English

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Cited by: 7 works

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