TY - JOUR

T1 - Analysis and comparison of two finite element algorithms for dislocation density based crystal plasticity

AU - Klusemann, Benjamin

AU - Svendsen, Bob

AU - Bargmann, Swantje

PY - 2013

Y1 - 2013

N2 - 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 γ -algorithm, the displacement u and glide system slips γα are global unknowns and determined via weak field relations. The non-dimensional densities of geometrically necessary dislocations ρ̄α are local quantities and solved for via a strong field relation. In the Q -algorithm, both the displacement uand dislocation densities ρ̄α are modeled as global, and the glide system slips γα 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.

AB - 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 γ -algorithm, the displacement u and glide system slips γα are global unknowns and determined via weak field relations. The non-dimensional densities of geometrically necessary dislocations ρ̄α are local quantities and solved for via a strong field relation. In the Q -algorithm, both the displacement uand dislocation densities ρ̄α are modeled as global, and the glide system slips γα 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.

KW - Engineering

KW - algorithmic variational

KW - boundary element

KW - dislocation density

KW - dual mixed

KW - gradient crystal plasticity

UR - http://www.scopus.com/inward/record.url?scp=84900538080&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/385ccfe6-1450-3b9a-997f-7c53cfa42157/

U2 - 10.1002/gamm.201310013

DO - 10.1002/gamm.201310013

M3 - Journal articles

AN - SCOPUS:84900538080

VL - 36

SP - 219

EP - 238

JO - GAMM Mitteilungen

JF - GAMM Mitteilungen

SN - 0936-7195

IS - 2

ER -