Multiscale Design of Vascular Plates

Abstract

Inspired by actuation mechanisms in plant structures and motivated by recent advances in electro-chemically driven micro-pumps, this paper is concerned with a novel concept for active materials based on distributed hydraulic actuation. Due to the similarity of the actuation principles seen in plants undergoing nastic motion, we refer to this class of active materials as nastic materials. We present a mechanical modeling approach for nastic materials representing the effects of pressure generation and fluid transport by incompressible eigenstrains. This model is embedded into a two-level macro/micro topology optimization procedure. On a macroscopic level, the integration of nastic material into a structural system is optimized. The placement and distribution of nastic material on a flexible substrate are optimized to generate target displacement and force distributions. On a microscopic level, the stress and strain generation is tailored to desired macroscopic material properties by optimizing the layout of vascular fluid channels embedded in an elastic matrix. For the layout optimization of vascular fluid channels, a novel topology optimization procedure is presented that models the effects of pressure along the fluid channels via an analogy with thermal conduction and convection. For this purpose an auxiliary heat transfer problem is solved. The macro-scale optimization procedure is studied for plate structures patterned by nastic materials in order to generate target bending and twist deformations. The results show the significant differences of the optimal distributions of active material depending on the strain model used for representing the actuation concept. The micro-scale vascular design methodology is verified with plane-stress examples. The results show that the layout of fluid channels can be optimized such that target strains are generated.

Plant-inspired adaptive structures and materials for morphing and actuation: a review

“…Especially, the study by Bruhn et al concluded that plant tissues are near-ideal osmotic pressure generators because they are composed of many small motor cells (capsules) with large surface to volume ratio and stiff cell wall reinforcements. To obtain a more efficient overall design, Dunn et al developed a multi-scale optimization scheme, which could optimize the design of cellular material with osmotic actuation at two different hierarchy levels [93]. At the macro-level, this approach optimizes the spatial distribution of the active, shape change components; and at the micro-level, it optimizes the distribution of the fluidic channels for a desired Eigen strain.…”

Pressure-actuated cellular structures

“…Potential cell topologies are limited to pentagonal and hexagonal cells as they maximize the inherent degrees of freedom, provide a smooth outer surface and minimize the total cell side length for a given cross sectional area. It is therefore rather surprising that some authors approach the design of pressurized cellular structures with the help of topology optimization [184,303]. Despite a predetermined topology, it is still of utmost importance that their geometry is described as efficiently as possible to simplify their simulation and optimization.…”