Minimum mass vascular networks in multifunctional materials

International Journal of Heat and Mass Transfer, 2009

The drive toward vascular smart materials calls for novel flow architectures that bathe and serve entire volumes and areas as uniformly as possible. Here, we show that vascular designs consisting of trees matched canopy to canopy can be configured so that they have two qualities: small flow resistance (w) and small volumetric flow nonuniformity (l). In the past, the only quality sought was small flow resistance. Two classes of architectures are explored: (a) matched trees with diagonal channels through the core and (b) matched trees with orthogonal channels. First, we show that flow architectures can be developed and selected for minimum flow nonuniformity alone. Second, in the w À l design space the best of designs (b) lie close to the best of designs (a), although the best of designs (b) offer slightly better configurations (low w and l) than the best of designs (a). Comparisons with similar architectures generated based on genetic algorithms show that the minimum global flow resistance w of designs (a, b) is 2-5 times smaller than the genetic-algorithm values. The flow nonuniformities l corresponding to the minimum w of designs (a, b) are 2-70 times smaller than the flow nonuniformities of the genetic-algorithm results.

Tissue Engineering Part A, 2010

Branched vascular networks are a central component of scaffold architecture for solid organ tissue engineering. In this work, seven biomimetic principles were established as the major guiding technical design considerations of a branched vascular network for a tissue-engineered scaffold. These biomimetic design principles were applied to a branched radial architecture to develop a liver-specific vascular network. Iterative design changes and computational fluid dynamic analysis were used to optimize the network before mold manufacturing. The vascular network mold was created using a new mold technique that achieves a 1:1 aspect ratio for all channels.

Arabian Journal for Science and Engineering, 2014

Your article is protected by copyright and all rights are held exclusively by King Fahd University of Petroleum and Minerals. This eoffprint is for personal use only and shall not be self-archived in electronic repositories. If you wish to self-archive your article, please use the accepted manuscript version for posting on your own website. You may further deposit the accepted manuscript version in any repository, provided it is only made publicly available 12 months after official publication or later and provided acknowledgement is given to the original source of publication and a link is inserted to the published article on Springer's website. The link must be accompanied by the following text: "The final publication is available at link.springer.com".

Biochemical Society Transactions, 2017

The vascular system is arguably the most important biological system in many organisms. Although the general principles of its architecture are simple, the growth of blood vessels occurs under extreme physical conditions. Optimization is an important aspect of the development of computational models of the vascular branching structures. This review surveys the approaches used to optimize the topology and estimate different geometrical parameters of the vascular system. The review is focused on optimizations using complex cost functions based on the minimum total energy principle and the relationship between the laws of growth and precise vascular network topology. Experimental studies of vascular networks in different species are also discussed.

Journal of Applied Physics, 2010

China Particuology, 2005

Constructal approach is a recent concept allowing to generate and optimize multi-scale structures, in particular, branching structures, connecting a microscopic world to a macroscopic one, from an engineer's point of view. Branching morphologies are found in many types of natural phenomena, and may be associated to some kind of optimization, expressing the evolutionary adaptation of natural systems to their environment. In a sense, the constructal approach tries to imitate this morphogenesis while short-cutting the trial-and-error of nature.

Journal of Applied Physics, 2010

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 weight͒ and the total channel volume are fixed. We show that the minimized peak stress is smaller when the channel volume ͑͒ is smaller and the vasculature is more complex, i.e., with more levels of bifurcation. Diminishing returns are reached in both directions, decreasing and increasing complexity. For example, when = 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.

Journal of Physics D: Applied Physics, 2007

Grid-shaped and tree-shaped flow architectures are being generated for use in vascularized materials with multiple functionality (self-healing, self-cooling, etc), based on the principle of the constructal law of evolutionary increase of flow access through the generation of better flowing configurations (designs). Here we investigate systematically the advantages of endowing the complex flow architecture with more freedom to morph. Four ways to increase design freedom are explored: multi-scale grids (one, two, three and four diameter sizes), multi-shape loops (square, triangular, hexagonal, rhombic), multi-shape bodies (hexagonal, square, rhombic) and vascularization with grids versus trees. We show that significant gains in global flow access are achieved as the number of optimized channel diameters increases. The most promising combinations of body and loop shapes are hexagonal bodies with triangular loops and square bodies with square loops. The tree-shaped architecture outperforms the grid, but it is recommendable only for stressed bodies in which the most likely location of the cracks is known ahead of time. The effect of body size on the global performance of vascularized multi-scale and multi-shape materials is documented. Diminishing returns and increasing robustness set in as the complexity of the optimized flow architectures increases.

Journal of Applied Physics, 2014

This paper is a proposal to embed tree-shaped vasculatures in a wall designed such that the wall withstands without excessive hot spots and peak stresses the intense heating and pressure that impinge on it. The vasculature is a quilt of square-shaped panels, each panel having a tree vasculature that connects the center with the perimeter. The vascular designs for volumetric cooling can be complemented by the shaping and distributing of channels for maximum strength and thermal performance at the same time. Numerical simulations of heat flow and thermal stresses in three directions show that it is possible to determine the optimal geometric features of configurations with radial channels and trees with radial and one level of bifurcations. The global performance is evaluated in terms of the overall thermal resistance and peak von Mises stresses. The dendritic design is superior under the studied thermal condition. V C 2014 AIP Publishing LLC.

International Journal of Heat and Mass Transfer

Construction of bioinspired vasculature in synthetic materials enables multi-functional performance via mass transport through internal fluidic networks. However, exact reproduction of intricate, natural microvascular architectures is nearly impossible and thus there is a need to create practical, manufacturable designs guided by multi-physics principles. Here we present a Hybrid Topology/Shape (HyTopS) optimization scheme for microvascular materials using the Interface-enriched Generalized Finite Element Method (IGFEM). This new approach, which can simultaneously perform topological changes as well as shape optimization of microvascular materials, is demonstrated in the context of thermal regulation. In the current study, we present a new feature that enables the optimizer to augment network topology by creating/removing microchannels during the shape optimization process. This task has been accomplished by introducing a new set of design parameters, which act analogous to the penalization factor in the Solid Isotropic Material with Penalization (SIMP) method. The analytical sensitivity for the HyTopS optimization scheme has been derived and the sensitivity accuracy is verified against the finite difference method. We impose a set of geometrical constraints to account for manufacturing limitations and produce a design which is suitable for large-scale production without the need to perform post-processing on the obtained optimum. The method is validated by active-cooling experiments on vascularized carbon-fiber composites. Finally, we compare various application examples to demonstrate the advantages of the newly introduced HyTopS optimization scheme over solely shape optimization for microvascular materials.