In Nature, biological materials such as nacre, bone, and dentin display an enhanced mechanical strength due to their structure characterized by hard inclusions embedded in a soft matrix. This structure has inspired the design of artificial materials with optimized properties. Thus, for given the mechanical properties of matrix and inclusions, it is fundamental to understand how the global observables, essentially strength, and ultimate strain are determined by the geometrical parameters of the inclusions. In this paper, we address this question by extending the two-dimensional random fuse model, which has been widely used to extract statistical properties of fracture processes, to the case of staggered stiff inclusions. We thus investigate numerically how emergent mechanical properties can be optimized by tuning geometrical dimensions and the arrangement of the inclusions. To do this, we adopt an optimization procedure based on an evolutionary algorithm to efficiently explore the parameter space and to determine the most favorable geometrical features of the inclusions for improved strength or ductility, or both. Various lattice sizes and volume fractions are considered. Depending on inclusion sizes and aspect ratios, composite strength or ultimate strain can be maximized, with the Pareto front for simultaneous optimization of the two being interpolated by a simple power law. Characteristic exponents for damage avalanche distributions are found to vary with respect to homogeneous structures, indicating increased fracture ductility simply due to optimized geometrical features. Our study indicates the possibility through structural optimization of creating staggered composites that allow significant advantages in terms of weight reduction and fuel consumption in automotive applications.

中文翻译：

---

使用随机保险丝模型的交错生物或仿生复合材料的进化算法优化

在自然界中，诸如珍珠母，骨头和牙本质的生物材料由于其结构具有嵌入软基质中的硬质夹杂物而具有增强的机械强度。这种结构启发了具有优化性能的人造材料的设计。因此，对于给定的基体和夹杂物的机械性能，基本的理解是如何通过夹杂物的几何参数确定整体可观测值，强度和极限应变的。在本文中，我们通过将二维随机熔丝模型扩展到交错的刚性夹杂物的情况，来解决这个问题，该模型已广泛用于提取断裂过程的统计特性。因此，我们在数值上研究了如何通过调整几何尺寸和夹杂物的排列来优化紧急机械性能。为此，我们采用基于进化算法的优化程序来有效地探索参数空间，并确定夹杂物最有利的几何特征，以提高强度或延展性，或两者兼而有之。考虑各种晶格尺寸和体积分数。根据夹杂物的大小和长宽比，可以通过简单的幂定律对用于同时优化两者的帕累托前沿进行最大化，从而使复合强度或极限应变最大化。发现破坏雪崩分布的特征指数随同质结构而变化，仅由于优化的几何特征表明断裂延展性增加。我们的研究表明，通过结构优化可以创造出交错的复合材料，从而在减轻重量和降低汽车应用的燃油消耗方面具有显着优势。