Assessment of Numerical Schemes for Solving Higher-Order Gradient Crystal Plasticity Model

Mechanical behavior of metallic materials is strongly influenced by the size effect at the micrometer scale. The conventional crystal plasticity theories, which are widely used for the meso-scale modeling of polycrystalline metals, do not represent the size effect because these theories cannot consider the accumulation of dislocations. Therefore, a higher-order gradient crystal plasticity model has been proposed for taking the dislocation information into account to describe the size effect [1]. In this model, geometrically necessary dislocations (GND) are introduced into a hardening function of the slip system. In this model, the following governing equations for displacement and GND density fields should be simultaneously solved. The high-order gradient crystal plasticity model, which couples the displacement and dislocation density fields, can be interpreted as a kind of mixed problem. In a mixed problem, the combination of analytical schemes for each field may strongly affect the analysis result. In fact, the finite element method (FEM) sometimes provides an improper solution in the higher-order gradient crystal plasticity analysis [2]. The reproducing kernel particle method (RKPM), which is a kind of meshfree method, is an alternative way to solve this model [3]. In this study, a quantitative investigation of effect of selection of element in the FEM and basis function in the RKPM on the high-order gradient crystalline plasticity analysis is demonstrated, and suitable numerical scheme to solve the higher-order gradient plasticity is discussed.

References

1. M. Kuroda and V. Tvergaard, A finite deformation theory of higher-order gradient crystal plasticity, Journal of the Mechanics and Physics of Solids, 56(8):2573–2584, 2008, https://doi.org/10.1016/j.jmps.2008.03.010.
2. M. Kuroda, On large-strain finite element solutions of higher-order gradient crystal plasticity, International Journal of Solids and Structures, 48(24):3382–3394, 2011, https://doi.org/10.1016/j.ijsolstr.2011.08.008.
3. Y. Tadano and N. Zenimoto, Kink strengthening mechanism due to multiple kink bands in long-period stacking ordered magnesium alloy, Computational Materials Science, 263:114428, 2026, https://doi.org/10.1016/j.commatsci.2025.114428.