Vascularized materials: Tree-shaped flow architectures matched canopy to canopy

Abstract

In this paper we develop flow architectures for “vascularizing” smart materials that have self-healing capabilities. The flow architectures are configured as two trees matched canopy to canopy. A single stream flows through both trees and bathes every subvolume (crack site) of the material. Several types of tree-tree configurations are optimized. Trees that have only one level of branching and bathe a rectangular domain have optimal external shapes that are nearly square. They also have optimal ratios of channel sizes before and after branching. Trees optimized on square domains perform nearly as well as trees on freely morphing rectangular domains. The minimized global flow resistance decreases slowly as the number of subvolumes increases. It is more beneficial to bathe the entire volume with a single (optimized) one-stream architecture than to bathe it with several streams that serve small clusters of volume elements. These conclusions are reinforced by an analytical optimization of the same class of architectures in the limit of a large number of assembled subvolumes. We also show that the freedom to morph the design and to increase its performance can be enhanced by using tree-tree architectures with more than one level of branching.