Prospect of quantum computing on Enhanced Strain Gradient Crystal Plasticity theory

A new branch of the Enhanced Strain Gradient Crystal Plasticity (ESGCP) theory is introduced, based on a quadratic energetic contribution associated with the gradient of the cumulative shear strain on each slip system, within a thermodynamically consistent framework for the formation of slip and kink bands in crystalline microstructures. Together with the recently proposed Nye-tensor-based ESGCP formulation, a new differential operator is developed for the solution of the corresponding nonlocal field equation (or higher-order balance equation). In both branches of the ESGCP theory, the higher-order modulus is intrinsically coupled to the evolving microstructural state of irradiated crystalline lattices during deformation. The ESGCP framework is employed to investigate the Hall–Petch (mean grain size) effect and is systematically compared with classical Strain Gradient Crystal Plasticity (CSGCP) models. The results reveal that, in contrast to CSGCP formulations where the grain-size effect continuously intensifies by the loading, the ESGCP models predict an enhanced grain-size sensitivity at low strain levels followed by a progressive attenuation at higher levels of loading. In addition, a novel quantum computing algorithm based on the quantum Fourier transform (QFT) is developed to solve the classical linear momentum balance equation within a fixed-point iteration scheme, while nonlocal field equations associated with the ESGCP and CSGCP models are addressed using a quantum finite difference approach. It is demonstrated that the proposed QFT-method achieves a poly-logarithmic computational speedup, offering significant advantages for high-resolution simulations of irradiated materials, where both numerical accuracy and computational efficiency are critical for reliable structural integrity assessments in nuclear power plant applications.