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Plant Biomechanics—A Natural Transition from Molecular to Organ Scale. Int J Mol Sci 2022; 23:ijms23147575. [PMID: 35886922 PMCID: PMC9320334 DOI: 10.3390/ijms23147575] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/17/2022] [Accepted: 07/07/2022] [Indexed: 02/04/2023] Open
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Wolff-Vorbeck S, Speck O, Langer M, Speck T, Dondl PW. Charting the twist-to-bend ratio of plant axes. J R Soc Interface 2022; 19:20220131. [PMID: 35730171 PMCID: PMC9214286 DOI: 10.1098/rsif.2022.0131] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
During the evolution of land plants many body plans have been developed. Differences in the cross-sectional geometry and tissue pattern of plant axes influence their flexural rigidity, torsional rigidity and the ratio of both of these rigidities, the so-called twist-to-bend ratio. For comparison, we have designed artificial cross-sections with various cross-sectional geometries and patterns of vascular bundles, collenchyma or sclerenchyma strands, but fixed percentages for these tissues. Our mathematical model allows the calculation of the twist-to-bend ratio by taking both cross-sectional geometry and tissue pattern into account. Each artificial cross-section was placed into a rigidity chart to provide information about its twist-to-bend ratio. In these charts, artificial cross-sections with the same geometry did not form clusters, whereas those with similar tissue patterns formed clusters characterized by vascular bundles, collenchyma or sclerenchyma arranged as one central strand, as a peripheral closed ring or as distributed individual strands. Generally, flexural rigidity increased the more the bundles or fibre strands were placed at the periphery. Torsional rigidity decreased the more the bundles or strands were separated and the less that they were arranged along a peripheral ring. The calculated twist-to-bend ratios ranged between 0.85 (ellipse with central vascular bundles) and 196 (triangle with individual peripheral sclerenchyma strands).
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Affiliation(s)
- Steve Wolff-Vorbeck
- Department for Applied Mathematics, University of Freiburg, 79104 Freiburg, Germany
| | - Olga Speck
- Plant Biomechanics Group @ Botanic Garden, Faculty of Biology, University of Freiburg, 79104 Freiburg, Germany.,Cluster of Excellence livMatS @ FIT - Freiburg Center for Interactive Materials and Bioinspired Technologies, University of Freiburg, 79104 Freiburg, Germany
| | - Max Langer
- Plant Biomechanics Group @ Botanic Garden, Faculty of Biology, University of Freiburg, 79104 Freiburg, Germany.,Cluster of Excellence livMatS @ FIT - Freiburg Center for Interactive Materials and Bioinspired Technologies, University of Freiburg, 79104 Freiburg, Germany
| | - Thomas Speck
- Plant Biomechanics Group @ Botanic Garden, Faculty of Biology, University of Freiburg, 79104 Freiburg, Germany.,Cluster of Excellence livMatS @ FIT - Freiburg Center for Interactive Materials and Bioinspired Technologies, University of Freiburg, 79104 Freiburg, Germany
| | - Patrick W Dondl
- Department for Applied Mathematics, University of Freiburg, 79104 Freiburg, Germany.,Cluster of Excellence livMatS @ FIT - Freiburg Center for Interactive Materials and Bioinspired Technologies, University of Freiburg, 79104 Freiburg, Germany
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Wolff-Vorbeck S, Speck O, Speck T, Dondl PW. Influence of structural reinforcements on the twist-to-bend ratio of plant axes: a case study on Carex pendula. Sci Rep 2021; 11:21232. [PMID: 34707194 PMCID: PMC8551206 DOI: 10.1038/s41598-021-00569-z] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2020] [Accepted: 10/14/2021] [Indexed: 12/02/2022] Open
Abstract
During biological evolution, plants have developed a wide variety of body plans and concepts that enable them to adapt to changing environmental conditions. The trade-off between flexural and torsional rigidity is an important example of sometimes conflicting mechanical requirements, the adaptation to which can be quantified by the dimensionless twist-to-bend ratio. Our study considers the triangular flower stalk of Carex pendula, which shows the highest twist-to-bend ratios ever measured for herbaceous plant axes. For an in-depth understanding of this peak value, we have developed geometric models reflecting the 2D setting of triangular cross-sections comprised of a parenchymatous matrix with vascular bundles surrounded by an epidermis. We analysed the mathematical models (using finite elements) to measure the effect of either reinforcements of the epidermal tissue or fibre reinforcements such as collenchyma and sclerenchyma on the twist-to-bend ratio. The change from an epidermis to a covering tissue of corky periderm increases both the flexural and the torsional rigidity and decreases the twist-to-bend ratio. Furthermore, additional individual fibre reinforcement strands located in the periphery of the cross-section and embedded in a parenchymatous ground tissue lead to a strong increase of the flexural and a weaker increase of the torsional rigidity and thus resulted in a marked increase of the twist-to-bend ratio. Within the developed model, a reinforcement by 49 sclerenchyma fibre strands or 24 collenchyma fibre strands is optimal in order to achieve high twist-to-bend ratios. Dependent on the mechanical quality of the fibres, the twist-to-bend ratio of collenchyma-reinforced axes is noticeably smaller, with collenchyma having an elastic modulus that is approximately 20 times smaller than that of sclerenchyma. Based on our mathematical models, we can thus draw conclusions regarding the influence of mechanical requirements on the development of plant axis geometry, in particular the placement of reinforcements.
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Affiliation(s)
- Steve Wolff-Vorbeck
- Department of Applied Mathematics, University of Freiburg, Hermann-Herder-Str. 10, 79104, Freiburg, Germany
| | - Olga Speck
- Plant Biomechanics Group @ Botanic Garden, Faculty of Biology, University of Freiburg, Schänzlestraße 1, 79104, Freiburg, Germany.,Cluster of Excellence livMatS @ FIT-Freiburg Center for Interactive Materials and Bioinspired Technologies, University of Freiburg, Georges-Köhler-Allee 105, 79110, Freiburg, Germany
| | - Thomas Speck
- Plant Biomechanics Group @ Botanic Garden, Faculty of Biology, University of Freiburg, Schänzlestraße 1, 79104, Freiburg, Germany.,Cluster of Excellence livMatS @ FIT-Freiburg Center for Interactive Materials and Bioinspired Technologies, University of Freiburg, Georges-Köhler-Allee 105, 79110, Freiburg, Germany
| | - Patrick W Dondl
- Department of Applied Mathematics, University of Freiburg, Hermann-Herder-Str. 10, 79104, Freiburg, Germany. .,Cluster of Excellence livMatS @ FIT-Freiburg Center for Interactive Materials and Bioinspired Technologies, University of Freiburg, Georges-Köhler-Allee 105, 79110, Freiburg, Germany.
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Wenig C, Dunlop JWC, Hehemeyer-Cürten J, Reppe FJ, Horbelt N, Krauthausen K, Fratzl P, Eder M. Advanced materials design based on waste wood and bark. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2021; 379:20200345. [PMID: 34334027 PMCID: PMC8330000 DOI: 10.1098/rsta.2020.0345] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Accepted: 03/11/2021] [Indexed: 06/13/2023]
Abstract
Trees belong to the largest living organisms on Earth and plants in general are one of our main renewable resources. Wood as a material has been used since the beginning of humankind. Today, forestry still provides raw materials for a variety of applications, for example in the building industry, in paper manufacturing and for various wood products. However, many parts of the tree, such as reaction wood, branches and bark are often discarded as forestry residues and waste wood, used as additives in composite materials or burned for energy production. More advanced uses of bark include the extraction of chemical substances for glues, food additives or healthcare, as well as the transformation to advanced carbon materials. Here, we argue that a proper understanding of the internal fibrous structure and the resulting mechanical behaviour of these forest residues allows for the design of materials with greatly varying properties and applications. We show that simple and cheap treatments can give tree bark a leather-like appearance that can be used for the construction of shelters and even the fabrication of woven textiles. This article is part of the theme issue 'Bio-derived and bioinspired sustainable advanced materials for emerging technologies (part 1)'.
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Affiliation(s)
- Charlett Wenig
- Department of Biomaterials, Max Planck Institute of Colloids and Interfaces, Am Mühlenberg 1, 14476 Potsdam, Germany
| | - John W. C. Dunlop
- Department of the Chemistry and Physics of Materials, Paris Lodron University of Salzburg, Morphophysics Group, Salzburg, Austria
| | - Johanna Hehemeyer-Cürten
- Department of Biomaterials, Max Planck Institute of Colloids and Interfaces, Am Mühlenberg 1, 14476 Potsdam, Germany
| | - Friedrich J. Reppe
- Department of Biomaterials, Max Planck Institute of Colloids and Interfaces, Am Mühlenberg 1, 14476 Potsdam, Germany
| | - Nils Horbelt
- Department of Biomaterials, Max Planck Institute of Colloids and Interfaces, Am Mühlenberg 1, 14476 Potsdam, Germany
| | - Karin Krauthausen
- Cluster of Excellence ‘Matters of Activity. Image Space Material’ at Humboldt Universität zu Berlin, Berlin, Germany
| | - Peter Fratzl
- Department of Biomaterials, Max Planck Institute of Colloids and Interfaces, Am Mühlenberg 1, 14476 Potsdam, Germany
| | - Michaela Eder
- Department of Biomaterials, Max Planck Institute of Colloids and Interfaces, Am Mühlenberg 1, 14476 Potsdam, Germany
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Langer M, Kelbel MC, Speck T, Müller C, Speck O. Twist-to-Bend Ratios and Safety Factors of Petioles Having Various Geometries, Sizes and Shapes. FRONTIERS IN PLANT SCIENCE 2021; 12:765605. [PMID: 34858462 PMCID: PMC8632552 DOI: 10.3389/fpls.2021.765605] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/27/2021] [Accepted: 10/20/2021] [Indexed: 05/09/2023]
Abstract
From a mechanical viewpoint, petioles of foliage leaves are subject to contradictory mechanical requirements. High flexural rigidity guarantees support of the lamina and low torsional rigidity ensures streamlining of the leaves in wind. This mechanical trade-off between flexural and torsional rigidity is described by the twist-to-bend ratio. The safety factor describes the maximum load capacity. We selected four herbaceous species with different body plans (monocotyledonous, dicotyledonous) and spatial configurations of petiole and lamina (2-dimensional, 3-dimensional) and carried out morphological-anatomical studies, two-point bending tests and torsional tests on the petioles to analyze the influence of geometry, size and shape on their twist-to-bend ratio and safety factor. The monocotyledons studied had significantly higher twist-to-bend ratios (23.7 and 39.2) than the dicotyledons (11.5 and 13.3). High twist-to-bend ratios can be geometry-based, which is true for the U-profile of Hosta x tardiana with a ratio of axial second moment of area to torsion constant of over 1.0. High twist-to-bend ratios can also be material-based, as found for the petioles of Caladium bicolor with a ratio of bending elastic modulus and torsional modulus of 64. The safety factors range between 1.7 and 2.9, meaning that each petiole can support about double to triple the leaf's weight.
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Affiliation(s)
- Max Langer
- Plant Biomechanics Group @ Botanic Garden, University of Freiburg, Freiburg, Germany
- Cluster of Excellence livMatS @ FIT – Freiburg Center for Interactive Materials and Bioinspired Technologies, University of Freiburg, Freiburg, Germany
- *Correspondence: Max Langer,
| | - Mark C. Kelbel
- Plant Biomechanics Group @ Botanic Garden, University of Freiburg, Freiburg, Germany
- Department of Microsystems Engineering – IMTEK, University of Freiburg, Freiburg, Germany
| | - Thomas Speck
- Plant Biomechanics Group @ Botanic Garden, University of Freiburg, Freiburg, Germany
- Cluster of Excellence livMatS @ FIT – Freiburg Center for Interactive Materials and Bioinspired Technologies, University of Freiburg, Freiburg, Germany
| | - Claas Müller
- Cluster of Excellence livMatS @ FIT – Freiburg Center for Interactive Materials and Bioinspired Technologies, University of Freiburg, Freiburg, Germany
- Department of Microsystems Engineering – IMTEK, University of Freiburg, Freiburg, Germany
| | - Olga Speck
- Plant Biomechanics Group @ Botanic Garden, University of Freiburg, Freiburg, Germany
- Cluster of Excellence livMatS @ FIT – Freiburg Center for Interactive Materials and Bioinspired Technologies, University of Freiburg, Freiburg, Germany
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