Bifurcation-dominated nonlinear bending behavior of laser peen forming: Analytical modeling and energy competition mechanism

Abstract

Surface morphology transitions driven by mismatch strains constitute a fundamental mechanical paradigm ubiquitous in manufacturing processes, such as panel forming. Laser peen forming (LPF) is an innovative and versatile forming process that incrementally shapes metallic panels into various types of surfaces through thousands of laser shocks spot-by-spot. However, the nonlinear bending behavior of LPF remains insufficiently understood. This study reveals that nonlinear deformation in LPF is a bifurcation-dominated nonlinear bending behavior driven by mismatch strain, which is fundamentally influenced by geometric nonlinearity. An analytical model was developed based on equivalent eigenstrain, enabling efficient predictions of nonlinear bending curvatures. Experimental characterization of 2024-T351 aluminum alloy plates across varying dimensions reveals clear bifurcation behavior, where the global morphology transitions from a double-curved to a single-curved configuration as the structure enters the nonlinear regime. Parametric studies using the analytical model provide a comprehensive understanding of the bifurcation behavior, elucidating that the dimensions of the plate significantly affect bifurcation behavior, as confirmed by experimental results. An energy-based analysis of a non-Euclidean plate reveals that bifurcation behavior arises from the competition between stretching and bending energies. An explicit bifurcation criterion is derived for identifying the critical bifurcation point. This work advances the fundamental understanding of mismatch strain-induced morphological transitions and establishes a theoretical framework for the design and stability control of shape morphing structures across different manufacturing processes and applications.