The exoskeleton of nearly all insects consists of a flexible core and a stiff shell. The transition between these two is often characterized by a gradual change in the stiffness. However, the functional significance of this stiffness gradient is unknown. Here by combining finite-element analysis and multi-objective optimization, we simulated the mechanical response of about 3000 unique gradients of the elastic modulus to normal contacts. We showed that materials with exponential gradients of the elastic modulus could achieve an optimal balance between the load-bearing capacity and resilience. This is very similar to the elastic modulus gradient observed in insect cuticle and, therefore, suggests cuticle adaptations to applied mechanical stresses; this is likely to facilitate the function of insect cuticle as a protective barrier. Our results further indicate that the relative thickness of compositionally different regions in insect cuticle is similar to the optimal estimation. We expect our findings to inform the design of engineered materials with improved mechanical performance.

中文翻译：

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进化分析支持的昆虫角质层分级特性的功能意义

几乎所有昆虫的外骨骼都由一个灵活的核心和一个坚硬的外壳组成。这两者之间的过渡通常以刚度的逐渐变化为特征。然而，这种刚度梯度的功能意义是未知的。在这里，通过结合有限元分析和多目标优化，我们模拟了大约 3000 个弹性模量的独特梯度对法向接触的机械响应。我们表明，具有弹性模量指数梯度的材料可以在承载能力和弹性之间实现最佳平衡。这与在昆虫角质层中观察到的弹性模量梯度非常相似，因此表明角质层适应施加的机械应力；这可能会促进昆虫角质层作为保护屏障的功能。我们的结果进一步表明昆虫角质层成分不同区域的相对厚度与最佳估计相似。我们希望我们的发现能够为具有改进机械性能的工程材料的设计提供信息。