Vascular structures for volumetric cooling and mechanical strength

When solid material is removed in order to create flow channels in a load carrying structure, the strength of the structure decreases. On the other hand, a structure with channels is lighter and easier to transport as part of a vehicle. Here, we show that this trade off can be used for benefit, to design a vascular mechanical structure. When the total amount of solid is fixed and the sizes, shapes, and positions of the channels can vary, it is possible to morph the flow architecture such that it endows the mechanical structure with maximum strength. The result is a multifunctional structure that offers not only mechanical strength but also new capabilities necessary for volumetric functionalities such as self-healing and self-cooling. We illustrate the generation of such designs for strength and fluid flow for several classes of vasculatures: parallel channels, trees with one, two, and three bifurcation levels. The flow regime in every channel is laminar and fully developed. In each case, we found that it is possible to select not only the channel dimensions but also their positions such that the entire structure offers more strength and less flow resistance when the total volume (or weight) and the total channel volume are fixed. We show that the minimized peak stress is smaller when the channel volume $(ϕ)$ is smaller and the vasculature is more complex, i.e., with more levels of bifurcation. Diminishing returns are reached in both directions, decreasing $ϕ$ and increasing complexity. For example, when $ϕ=0.02$ the minimized peak stress of a design with one bifurcation level is only 0.2% greater than the peak stress in the optimized vascular design with two levels of bifurcation.