Analysis and comparison of two finite element algorithms for dislocation density based crystal plasticity
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In: GAMM Mitteilungen, Vol. 36, No. 2, 2013, p. 219-238.
Research output: Journal contributions › Journal articles › Research › peer-review
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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 -