The deformation mode transition of indented elastic thin shell induced by localized curvature imperfection

Abstract

Numerous studies have indicated that spherical thin shells exhibit imperfection sensitivity under external pressure or top-indentation, which can greatly impair their loading strength and stability. In this paper, a surprising shift in buckling behavior is achieved for elastic thin shell by locally manipulating the annular imperfection of curvature on a sphere, which reverses the harmfulness wrought by defects. Combined with experiments and simulations, four distinct deformation modes (Near-perfect, Negative, Transitional, and Positive) are detected to exist in the studied parameter space, widely altering the indentation response from notable snap-through to rigid performance without initial bifurcation. Moreover, these diverse characteristics can be successfully captured by a novel theory proposed for solving the axisymmetric behavior of finite curved surface in elasticity. The comprehensive analysis of the intrinsic mechanism of deformation mode transition reveals the significant role of the geometry parameters of imperfections. It turns out that the depth of imperfection is crucial for the mode evolution, while the defect width and curvature radius control the mechanical properties in detail to achieve optimal performance. The design of localized curvature defect gifts the spherical shell with multiple functions that cannot be possessed by itself, including high stiffness and response peak by Positive mode, extremely negative stiffness and post-buckling obstruction by Negative mode, and enhanced energy absorption by Transitional mode. These advantages provide a new possibility for improving the performance of thin shells, and open up a broad prospect for potential applications in the future.