A dual-length-scale gradient crystal plasticity framework: Finite-element implementation and validation against single-crystal copper micro-bending experiments

This paper develops a gradient-enhanced finite-strain crystal plasticity framework with two distinct intrinsic length scales associated with lattice incompatibility and higher-order orientation gradients. The formulation is built on a curvature-based description of elastic rotation and its associated incompatibility measures, and it provides a clear separation between dislocation-driven mechanisms and curvature-gradient (disclination-type) mechanisms within a unified kinematic setting. A differential-geometric interpretation is used to connect these measures to torsion- and curvature-type incompatibilities, thereby clarifying the physical meaning of the additional fields and the origin of size effects. The constitutive structure is posed within a thermodynamically consistent internal-variable framework, yielding coupled relations for classical stress and higher-order stress measures, along with the corresponding balance laws at multiple scales. Analytical validation is established through a set of canonical boundary-value problems. A benchmark single-crystal strip in simple shear demonstrates size-dependent hardening under constrained deformation and reveals boundary-layer formation. Complementary analytical studies treat torsion of a cylindrical bar, bending of a crystal plate, and a bicrystal tilt boundary, providing closed-form reductions that highlight how the two length scales govern the localization of orientation gradients and the spatial organization of defect-related fields. A finite-element implementation is then presented, including an integration-point constitutive update and a mixed variational formulation tailored to the higher-order structure of the theory. Numerical simulations of cantilever micro-bending quantify thickness-dependent strengthening and distinguish the roles of curvature-amplitude strengthening versus curvature-gradient regularization. Finally, the computed micro-bending trends are compared with reported single-crystal copper micro-beam experiments, demonstrating that the proposed two-length framework captures the primary thickness dependence while offering a unified continuum route to incorporate defect geometry into predictive crystal plasticity simulations.