Minimum mass vascular networks in multifunctional materials

Abstract

A biomimetic analysis is presented in which an expression for the optimum vessel diameter for the design of minimum mass branching or vascular networks in engineering applications is derived. Agreement with constructal theory is shown. A simple design case is illustrated and application to more complex cases with branching networks of several generations discussed. The analysis is also extended into the turbulent flow regime, giving an optimization tool with considerable utility in the design of fluid distribution systems. The distribution of vessel lengths in different generations was also found to be a useful design variable. Integrating a network into a structure is also discussed. Where it is necessary to adopt a non-optimum vessel diameter for structural integration, it has been shown that small deviations from the minimum mass optimum can be tolerated, but large variations could be expected to produce a punitive and rapidly increasing mass penalty.

Interactions between propagating cracks and bioinspired self-healing vascules embedded in glass fibre reinforced composites

“…However, if the damage were autonomously healed by entities embedded within the composite component, then conservative designs could be avoided, leading to lighter more fuel efficient transport. Of course, the embedment of functional components should not impart a mass penalty of their own for this philosophy to hold [4]. At present, it should be recognised that composite structures are designed based on strength and stiffness criteria rather than being fracture mechanics driven.…”

Self-healing polymers and composites

“…of microvascular self-healing systems. 144,145 However, the complexity of many of these optimal design conditions for microvascular systems would likely require extremely sophisticated fabrication techniques that are currently technologically unavailable or too elaborate to be practical. Therefore, only a few vascular architectures described in these reports have been experimentally demonstrated.…”

“…[133][134][135]228 Additionally, an increased mass penalty is observed when incorporating microvascular networks throughout a polymer matrix, 153 but mass penalties can potentially be reduced by adjusting the vascular network architecture. 144,145 Several approaches to self-healing involve the development of new polymer matrices where the healing functionality is inherently part of the virgin material (for example, see the above section on polymers that heal via bond reformation). While these systems do not contain traditional healing additives, and therefore cannot be discussed in the context of virgin property changes, it is at least important to consider whether or not their virgin properties are adequate enough to substitute for the traditional engineering polymers they intend to replace.…”

Constructal vascularized structures

“…Advanced capabilities such as self-healing and selfcooling require bathing the entire volume with coolant uid or healing agent [1][2][3][4][5], which can be achieved by vascularization. In addition of being necessary for the advanced capabilities, vascularization is also essential to decrease the resistances of the distribution of energy, goods and water [1,6,7].…”