Gradient-enhanced visco-plastic models: Advancing localization and deformation analysis in toothpaste flow and hollow sphere deformation

This study explores the incorporation of gradient-enhanced visco-plastic models to address the limitations of traditional visco-plastic formulations in capturing size-dependent and localized deformation behaviors. By introducing second-gradient terms, the proposed framework accounts for non-local effects and smoothens discontinuities in stress and deformation profiles, which are critical for accurately modeling materials with complex microstructures. Analytical solutions are derived for benchmark problems, including the deformation of a hollow sphere and toothpaste-like flow, demonstrating the enhanced predictive capabilities of the gradient-enhanced models. Numerical analyses further validate these formulations, highlighting their ability to stabilize computations and provide physically realistic stress distributions under highly localized loading conditions. The results reveal the significance of the gradient coefficient in influencing stress diffusion and plastic strain localization, emphasizing its role in material design and engineering applications. The study establishes robust theoretical and computational foundations for gradient-enhanced visco-plastic models, offering new insights into material behavior at micro and meso-scales, with implications for advanced manufacturing and processing technologies.