The mechanics of triply periodic minimal surfaces (TPMSs) with three-dimensional (3D) graphene foams are systematically studied to understand the effects of structure and size on the mechanical properties, for example, elasticity, strength, and fracture. The design of lightweight open-shell porous solid materials with TPMSs has shown excellent and tunable load-bearing properties. However, fracture properties and their relations with surface topologies are largely unknown. Utilizing reactive molecular dynamics simulations, here we investigate the elastic and fracture properties of three different surface topologies with 3D graphene foams: P (primitive), D (diamond), and G (gyroid), called Schwarzites. Models with different lattice sizes are utilized to derive power laws, which can connect the properties along different sizes to shed light on the multiscale mechanics of TPMSs. Our study provides a systematic understanding of the relation between TPMS topologies and their mechanical properties, including failure mechanisms of graphene foams, opening opportunities to explore designable structures with tailored properties.

中文翻译：

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三维石墨烯泡沫的三重周期最小曲面的多尺度力学

系统地研究了具有三维（3D）石墨烯泡沫的三重周期性最小表面（TPMS）的力学，以了解结构和尺寸对机械性能（例如弹性，强度和断裂）的影响。带有TPMS的轻质开壳多孔固体材料的设计显示了出色的可调节承载特性。但是，断裂特性及其与表面拓扑的关系在很大程度上是未知的。利用反应分子动力学模拟，在这里我们研究3D石墨烯泡沫的三种不同表面拓扑的弹性和断裂特性：P（原始），D（金刚石）和G（陀螺仪），称为Schwarzites。利用具有不同晶格尺寸的模型来推导幂律，可以将不同尺寸的属性连接起来，以揭示TPMS的多尺度机制。我们的研究提供了对TPMS拓扑及其机械性能之间关系的系统理解，包括石墨烯泡沫的破坏机理，为探索具有定制性能的可设计结构提供了机会。