打印非欧几里得实体
Printing non-Euclidean solids
摘要：
具有非欧几里德参考度量的几何受挫固体在生物学中普遍存在，并且在技术应用中变得越来越重要。通常，它们通过质量的表面增长（如树木生长或水坝建设）获得不相容的目标配置。我们使用不相容表面生长的力学来表明，可以微调沉积过程中产生的几何挫折，以确保系统在生理（或工作）条件下的特定行为。作为一个例子，我们获得了一个明确的动脉3D打印协议，它保证了在不均匀载荷下的应力均匀性，以及爆炸性植物，允许通过一次切割完全释放残余弹性能量。有趣的是，在这两种情况下，达到生理目标需要不相容性具有拓扑（全局）组件。
英文摘要：
Geometrically frustrated solids with non-Euclidean reference metric are ubiquitous in biology and are becoming increasingly relevant in technological applications. Often they acquire a targeted con- figuration of incompatibility through surface accretion of mass as in tree growth or dam construction. We use the mechanics of incompatible surface growth to show that geometrical frustration develop- ing during deposition can be fine-tuned to ensure a particular behavior of the system in physiological (or working) conditions. As an illustration, we obtain an explicit 3D printing protocol for arteries, which guarantees stress uniformity under inhomogeneous loading, and for explosive plants, allowing a complete release of residual elastic energy with a single cut. Interestingly, in both cases reaching the physiological target requires the incompatibility to have a topological (global) component.
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