Functional branching morphology of arborescent columnar cacti / Biomimetic optimization for branched fiber-reinforced composites

Datum

16.04.2012

Zeit

11:10 - 12:10

Sprecher

Hannes Schwager

Zugehörigkeit

TU Dresden, Institut für Botanik

Sprache

en

Hauptthema

Mathematik

Andere Themen

Biologie, Mathematik

Beschreibung

In contrast to trees, the ramifications of arborescent columnar cacti possess pronounced constrictions at the junction between branch and stem. Beneath the succulent cortex, the cactus wood, normally forming a broad cylinder of wood lamellae [2,3,4], is reduced to a compact socket with distinct indentations on the adaxial and abaxial side. Notwithstanding the common theory that neckings in regions of the high bending stress represent structural weak points, the ramifications of columnar cacti provide sufficient stability to the side shoots, even under superposition of static and dynamic loading. To explain this counterintuitive structure-function relationship, detailed knowledge of anatomy and material properties on all hierarchical levels is required. Branched specimens collected in the botanical gardens of the TU Dresden and the University of Freiburg were examined concerning the functional morphology and the arrangement of the constituent tissues. Trunk and ramification segments were prepared by enzymatic maceration to conceive the axial course of the vascular bundles. In addition, the fiber orientation inside the ramification was analyzed by modern optical and radiographic means (e.g. 3D-laserscanning, micro-focus computer tomography). Based on these studies, representative geometric models of the selected species were created with Computer Aided Design (CAD) software and evaluated in Finite Element Analysis (FEA). The required elastic constants for these models were determined in uniaxial material tests on the four main tissues. The parenchymatous pith and cortex were tested in compression tests, whereas the wood and the cuticle were tested in tension tests. Under self-weight conditions, the results showed that the load adaptation does not follow the simple rule of stress homogenisation and minimisation by material accumulation in highly stressed areas [1,5]. The succulent cortex limits the secondary growth of the vascular tissue, hence it seems more advantageous to tune the tension stress by geometric changes to already predominant fiber directions. Another surprising detail is that the compression stress on the abaxial side is partly dissipated by the parenchymatous cortex. Under lateral wind drag, the tension stress maximum in the vascular tissue occurs in the same region as under dead load and again the cortex partly dissipates the compression stress on the backside. These results indicate that load-adaptation in cactus ramifications is realized by a combination of shape optimization and fiber arrangement. The biomimetic transfer of the design principles might help to develop alternative concepts for branched light-weight fiber-reinforced composites especially for structures with limited design space.

Links

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Letztmalig verändert: 13.04.2012, 11:51:13