Abstract：Many natural fruits and vegetables adopt an approximately spheroidal shape and are characterized by their distinct undulating topologies. We demonstrate that various global pattern features can be reproduced by anisotropic stress-driven buckles on spheroidal core/shell systems, which implies that the relevant mechanical forces might provide a template underpinning the topological conformation in some fruits and plants. Three dimensionless parameters, the ratio of effective size/thickness, the ratio of equatorial/polar radii, and the ratio of core/shell moduli, primarily govern the initiation and formation of the patterns. A distinct morphological feature occurs only when these parameters fall within certain ranges: In a prolate spheroid, reticular buckles take over longitudinal ridged patterns when one or more parameters become large. Our results demonstrate that some universal features of fruit/vegetable patterns (e.g., those observed in Korean melons, silk gourds, ribbed pumpkins, striped cavern tomatoes, and cantaloupes, etc.) may be related to the spontaneous buckling from mechanical perspectives, although the more complex biological or biochemical processes are involved at deep levels.

    应力是影响有机与无机世界里各种生长过程的重要因素，因此是生长与形态研究所必须考虑的关键因素。近年来，国际上关于应力驱动结构失稳在薄膜上引起的各种花样的研究取得了许多重要的进展。这些研究对于理解各种花样包括皱纹、材料断裂、薄膜表面形貌提供了深入的认识。但是，在这些工作了所涉及的都是有开放边界的曲面或平面，它们在拓扑学上都是亏格数为1的表面。对于亏格数为0的闭合曲面上的应力屈曲形态及其在理解自然方面的意义则鲜有涉及。

该系列的最新研究工作以“Stress-driven buckling patterns in spheroidal core/shell structures”为题发表在美国《国家科学院院刊》 （PNAS 105，1932，2008）上 。