Regime-Dependent Elastic Displacement in Bio-Inspired Parametric Kirigami Structures: An Experimental Study of Geometric Parameter Effects

Biological thin-sheet systems, including leaves, insect wings, and flowering organs, achieve adaptive deformation through distributed compliance, segmentation, curvature, and controlled opening. Kirigami offers a bio-inspired route for translating such deformation logics into programmable thin-sheet surfaces; however, the geometric parameters that most strongly influence elastic displacement remain insufficiently quantified, especially across different loading regimes. This study investigates Bio-Inspired Regime-Dependent Parameter Selection in Parametric Kirigami through twenty-five laser-cut specimens spanning five boundary shapes and three thermoplastic substrates. Specimens were tested under two contrasting regimes: quasi-static tensile loading and gravity-drape loading. Elastic displacement was measured under eight-point boundary fixation and analyzed using regime-separated Pearson correlations, Bonferroni-corrected significance testing (α/18 = 0.0028), and shape-controlled partial correlations. Under tensile loading, the Number of Offsets (r = 0.807), Segments per Offset (r = −0.603), and outer-boundary void perimeter (r = 0.621) showed the strongest Bonferroni-robust associations with displacement. Under gravity-drape loading, effects were weaker and more curvature-sensitive, indicating that parameter relevance is not universal but regime-dependent. Within the tested parametric design space, the study provides an experimentally grounded basis for selecting Kirigami geometric parameters in thin-sheet structures whose adaptive deformation logic is analogous to compliant systems found in nature.