• Interaction and multiscale mechanics
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• v.1 no.4
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• pp.423-435
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• 2008

This paper employs the reproducing kernel (RK) approximation for evaluation of field theory-based incompatibility tensor in a polycrystalline plasticity simulation. The modulation patterns, which is interpreted as mimicking geometrical-type dislocation substructures, are obtained based on the proposed method. Comparisons are made using FEM and RK based approximation methods among different support sizes and other evaluation conditions of the strain gradients. It is demonstrated that the evolution of the modulation patterns needs to be accurately calculated at each time step to yield a correct physical interpretation. The effect of the higher order strain derivative processing zone on the predicted modulation patterns is also discussed.

• Interaction and multiscale mechanics
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• v.2 no.1
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• pp.1-14
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• 2009

This paper proposes an interaction field concept based on the field theory of plasticity. Relative deformation between two arbitrary scales, e.g., macro and micro fields, is defined which can be implemented in the crystal plasticity-based constitutive framework. Differential geometrical quantities responsible for describing dislocations and defects in the interaction field are obtained, based on which dislocation density and incompatibility tensors are further derived. It is shown that the explicit interaction exists in the curvature or incompatibility tensor field, whereas no interaction in the torsion or dislocation density tensor field. General expressions of the interaction fields over multiple scales with more than three scale levels are derived and implemented into the present constitutive equation.

• Interaction and multiscale mechanics
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• v.2 no.1
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• pp.15-30
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• 2009

The theoretical framework of the interaction fields for multiple scales based on field theory is applied to one-dimensional problem mimicking dislocation substructure sensitive intra-granular inhomogeneity evolution under fatigue of Cu-added steels. Three distinct scale levels corresponding respectively to the orders of (A)dislocation substructures, (B)grain size and (C)grain aggregates are set-up based on FE-RKPM (reproducing kernel particle method) based interpolated strain distribution to obtain the incompatibility term in the interaction field. Comparisons between analytical conditions with and without the interaction, and that among different cell size in the scale A are simulated. The effect of interaction field on the B-scale field evolution is extensively examined. Finer and larger fluctuation is demonstrated to be obtained by taking account of the field interactions. Finer cell size exhibits larger field fluctuation whereas the coarse cell size yields negligible interaction effects.