Analysis and comparison of two finite element algorithms for dislocation density based crystal plasticity. Issue 2 (7th October 2013)

• Record Type: Journal Article
• Authors: Klusemann, Benjamin; Svendsen, Bob; Bargmann, Swantje
• Is Part Of: Mitteilungen der Gesellschaft für Angewandte Mathematik und Mechanik. Volume 36:Issue 2(2013)
• Page Start: 219
• Page End: 238
• Publication Date: 2013-10-07
• Subjects: Mathematics -- Periodicals; Mechanics, Applied -- Periodicals; 510.5
• DOI: 10.1002/gamm.201310013
• Languages: English
• ISSNs: 0936-7195

Abstract

<abstract abstract-type="main" xml:lang="en"> <title>Abstract</title> <p>The purpose of the current work is the formulation and comparison of two finite element algorithms for a dislocation density based crystal plasticity model. We study multiscale inelastic materials whose behavior is influenced by the evolution of inelastic microstructure and the corresponding material or internal lengthscales. The work is an extension of the first investigation in Klusemann et al. [1] which was limited to a one‐dimensional bar. In the <italic>γ</italic> ‐algorithm, the displacement <bold><italic>u</italic></bold> and glide system slips <italic>γ<sub>α</sub></italic> are global unknowns and determined via weak field relations. The non‐dimensional densities of geometrically necessary dislocations <italic>∼<sub>α</sub></italic> are local quantities and solved for via a strong field relation. In the <italic>Q</italic> ‐algorithm, both the displacement <bold><italic>u</italic></bold>and dislocation densities <italic>∼<sub>α</sub></italic> are modeled as global, and the glide system slips <italic>γ<sub>α</sub></italic> as local. As it turns out, both algorithms generally predict the same microstructural behavior on a single crystal level. However, for a polycrystal the two solution strategies predict different material behaviors due to the formulation‐dependent representation of the boundary conditions. The introduction of a boundary layer in the model leads to good agreement between both algorithms for single and polycrystal simulations. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)</p> </abstract>