Tansley insight Functional morphology of plants – a key to biomimetic applications

Learning from living organisms has emerged from a mainly curiosity-driven examination, where helpful functions of biological structures have been copied, into systematic biomimetic approaches that transfer a targeted function and its underlying principles from the biological model to a technical product. Plant biomimetics is based on functional morphology, which combines the knowledge gained from the morphology, anatomy and mechanics of plants and makes a statement about their form-structure-function relationship. Since the functional morphology of plants has become key to biomimetic applications, we present its central role in deciphering the functional principles that can be applied to engineering solutions. We consider that the future of biomimetics will include bioinspired developments that will contribute to better sustainability than that achieved by conventional products.


I. Introduction
A brief historical outline In the following, we provide a brief historical outline of biomimetics up to current state-of-the-art products. With reference to the topic of the article, we limit the examples to plant-inspired innovations. Based on an historical starting position at the beginning of the early modern period in which biology and technology were strictly separated (Fig. 1a), learning from living organisms has formed part of human cultural evolution. In its early beginnings, it was a mainly curiositydriven approach, the helpful functions of biological structures being copied using little modified natural and often biobased materials. Although well known for his various flying machines, the 15 th century Italian polymath Leonardo da Vinci was also interested in plants. He wrote in his notebook that 'all the branches of a tree at every stage of its height when put together are equal in thickness to the trunk'. Since then, da Vinci's Rule of Trees has inspired many scientists to develop various simulations and models (Eloy, 2011). On the occasion of the construction of Crystal Palace for the London World Exhibition in 1851, Sir Joseph Paxton invented the so-called 'Paxton gutters' used to drain the rain and condensation in the roof cross-bracing, which was inspired by the leaf structures of the giant water lily (Victoria amazonica).
During the 19 th century, Sir George Cayley developed aerial vehicles inspired by the gliding flight of seeds and fruits and Otto This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
Lilienthal constructed various bird-inspired gliders for manned flight (Fig. 1b). Furthermore, in 1904, Ignaz 'Igo' Etrich and F. X. Weis developed a manned flying wing inspired by the selfstabilizing gliding seeds of the zanonie, a tropical cucurbit (Alsomitra macrocarpa). In 1917, D'Arcy Wentworth Thompson published his book 'On Growth and Form', which describes various biological structures and (forming) processes on the basis of physical and mathematical principles. During the middle of the 20 th century, George de Mestral registered a patent for the hook-and-loop fastener under the brand Velcro ® , which consists of a hook strip inspired by burdock burs and a loop strip inspired by animal fur (Vincent et al., 2006). Barthlott & Neinhuis (1997) deciphered the principle of the self-cleaning surfaces of lotus leaves (Nelumbo nucifera), which was patented in 1998 under the brand name Lotus-Effect ® (Fig. 2a). By integrating the wax-repairing function of lotus leaves and the slippery surface of pitcher plants, Wang et al. (2016) developed bioinspired slippery liquid-infused porous surface (X-SLIPS) coatings with a thermal healing function (Fig. 1c). Inspired by the growth rules of trees, Mattheck (2006) developed the optimization tool CAO (Computer Aided Optimization) to design technical components having an optimized shape with minimized notch stresses (Fig. 1d). The CAO-optimized orthopaedic screw can withstand 5 million load cycles in contrast to the nonoptimized screw in which fatigue cracks occur after only 220 000 load cycles (Fig. 1e).  In an envisioned future, the boundary between biology and technology will have dissolved and a new boundary will occur with channels that select for a product's contribution to sustainability.

Current state-of-the-art
A Google Scholar search has revealed that the number of publications and patents with the terms 'biomimetics', 'bionics', 'bioinspiration' and 'biomimicry' grew exponentially from 1995 to 2020 (Supporting Information Fig. S1). In 2013, Lepora et al. analysed the 100 most common topics in biomimetics from the titles in a database of around 18 000 publications on biomimetics. In addition to some inevitable basic terms such as biomimetic, based, bionic, inspired or application, the following topics were among the top 10: robot, model, design, control and human. The word 'biological' was placed 25 and 'fish' was placed 51, whereas the terms 'plant', 'animal' or 'sustainable development' were not listed. The topics raised by Lepora et al. (2013) are still relevant today but have been supplemented by some new application areas, especially with a focus on plant biomimetics. The development of additive manufacturing has opened up a whole new world of possibilities: building from the small to the large, as in nature, allows us literally to 'grow' technical components. Using functionally graded prototyping, Oxman et al. (2011) produced variable-density graded concrete and cement foams inspired by the gradients found in palm trees and bones. In the field of architecture, a variety of biomimetic building skins have been created based on the functional principles of plant movement (Correa et al., 2020). The movement of the façade shading system Flectofin ® (Fig. 2b) is based on the principle of lateral-torsional buckling, transferred from the opening mechanism of the perch of Strelitzia flowers (Lienhard et al., 2011). The functional principles of wound sealing in plants have been successfully transferred to a self-sealing coating of pneumatic systems (Rampf et al., 2013) and a self-healing polymer with shape-memory effect (Yang et al., 2018).
Moreover, scientists are currently studying the development, structure and properties of multifunctional complex plant surface structures at a fundamental level and are creating functional polymeric materials and surfaces based on the functional principles of plants. Cuticles are concept generators for the regulation of water permeability (Mulama et al., 2019), structural colours (Moyroud et al., 2017) and sticky or nonfriction surfaces (Bergmann et al., (2) scanning electron micrograph of a self-cleaning leaf surface that shows a microrough epidermis with nanorough wax crystals; (3) the functional principle is the creation of a minimized contact area based on a water-repellent microrough epidermis (light blue) with nanostructured and hydrophobic wax crystals (magenta), which, in combination with the surface tension of the water droplets (blue), can wash off dirt particles (orange); (4) equations describing the effect of roughness to contact angles, whereby self-cleaning surfaces show contact angles with water of typically c. 150°; (5) self-cleaning products with the above-mentioned functional principle bearing the Lotus-Effect ® trademark; (6) rain drops repelling dirt from faç ades painted with Lotusan ® . (b) Technology pull process of the adaptive faç ade shading system Flectofin ® . (1) What design will produce hinge-less kinematics without gliding parts for deployable systems in architecture?; (2) the perch of the bird-of-paradise flower is an elastic, highly resilient deformation system; (3) the functional principle is a lateral-torsional buckling; (4) the kinematic structure is simulated with finite element modelling; (5) technical applications consist of one or two laminae and one backbone being activated by bending; (6) closed state of Flectofin ® lamellae (after Speck et al., 2017). 2020). The moving-by-growing abilities of climbing plants have become models for the development of low-mass and low-volume robots capable of anchoring themselves, negotiating voids and more generally climbing (Fiorello et al., 2020;Mazzolai et al., 2020). The vision of combining nature and technology has also been achieved through the development of dynamic nonequilibrium materials systems. Research concepts include energyautonomous materials systems (Deng & Walther, 2020), the longevity of system functions  and adaptive (inter)active materials systems (Esser et al., 2019). Since the turn of the millennium, concomitantly with the proclamation of the Anthropocene made popular by the publication of Crutzen & Stoermer (2000), a call has gone out for biomimetic products, which ought to contribute to a more sustainable future (Benyus, 2002). In recent years, increased attention has been drawn to societal challenges in terms of sustainability assessment and the investigation of psychological, philosophical and ethical implications of biomimetic materials systems MacKinnon et al., 2020).
In this Tansley insight article, we wish to highlight the way in which plant-inspired research in biomimetics has developed over recent years. Since the functional morphology of plants has become key to biomimetic applications, we present its central role in deciphering the functional principles that can be applied to engineering solutions. Finally, we draw conclusions and describe future perspectives and potentials of plant biomimetics.

II. Biomimetic approaches
Box 1 shows that systematic learning from recent and fossil organisms leading to technical applications is diverse in terms of the selected attribute and the respective application field. Various step-by-step developmental approaches of biomimetics and bioinspiration have emerged over the last few years (Speck & Speck, 2008;Goel et al., 2014;ISO 18458:2015ISO 18458: , 2015. The biomimetic approach 'biology push process' (= bottom-up approach) (Fig. 2a) and the biologically inspired design (BID) approach with a 'solutions-based analogical process' both start from biological questions. By contrast, the initiation points of the biomimetic 'technology pull process' (= top-down approach) (Fig. 2b) and the BID approach 'problem-driven analogical process' both begin with a technical challenge that might be solved with the help of biological knowledge. All these approaches have in common that a functional principle is identified, abstracted and later transferred to the technical product (Fayemi et al., 2017;Speck et al., 2017). In the case of plant biomimetics, the functional morphology of the selected model plant is essential for deciphering the functional principle of interest and for achieving the targeted function in the technical product. The step from a functional principle to the abstraction is an iterative process that leads not only to an engineering-compatible language in the form of functional models, mathematical descriptions, numerical simulations, circuit diagrams or blueprints, but also to a deeper understanding of the biological model. Learning from nature also has the characteristics that: it never provides a simple copy of the biological model; it works on the basis of existing physical (including biomechanics), chemical and mathematical laws; it is especially promising when physicochemical processes are involved; it creates innovations (biomimetics); it helps to establish a deeper understanding of the biological models (reverse biomimetics); and it is not a later reinterpretation of a purely technical product that is then designated as having been bioinspired (a posteriori biomimetization) .

III. Functional morphology of plants
We are aware that the terms morphology, anatomy, biomechanics and functional morphology are used in a variety of ways. Therefore, we will now define some basic terms that are important for a common understanding in functional plant morphology. Morphology comprises the macroscopically visible characteristics, such as geometry, shape, size or colour of plant organs (root, stem, leaf and flower). Anatomy includes the microscopically visible internal structures at the tissue, cellular and subcellular level observed by using various imaging techniques and typically requiring invasive sample preparation such as sectioning. Biomechanics analyses the mechanical properties and processes of plants at various hierarchical levels from the whole organism to plant organs, tissues, cells and their cell walls or organelles. Functional morphology combines the knowledge gained from the morphology, anatomy and biomechanics of the respective plant or plant part and makes a statement about the form-structure-function relationship (Fig. 3).
The mechanical performance of plants depends on both their geometrical setup and material properties (Box 2; Niklas, 1992;Niklas & Spatz, 2012). Axial, flexural and torsional rigidity quantify the resistance of a structure to elastic deformation by tension, bending and torsion, respectively. The ultimate tensile, flexural and torsional strength (i.e. strength at fracture) refer to the maximal capacity of a structure to resist tensile, bending and torsional loads. The relevant geometrical features include the area perpendicular to the tensile direction and, under bending or torsional load, the axial or polar second moment of area. The material properties include the stress-strain relationship in the linear-and the nonlinear-elastic range under tension, bending and torsion. The stress-strain relationship in the linear-elastic range is quantified by the elastic moduli. In all load cases, rigidity is given as the product of material property and geometrical setup. The rigidity of entire plant organs depends on their geometry, shape and size and their 'overall' elastic modulus, which results from the three-dimensional arrangement of various tissues with greatly varying mechanical properties. Box 2 provides a list of the most important plant tissues and their range of elastic moduli. The huge variety of potential combinations thus gives insight not only into the origin of the plethora of body plans of plants, but also into the ability of plants to undergo rapid responses and long-term evolutionary adaptation to changing environmental conditions. However, functional morphology is more than the sum of all information about morphological, anatomical and biomechanical properties, because these insights are interpreted against the background of a presumed function of the selected plant organ. The problem that we cannot experimentally determine the function of a matter belongs to the 'causa finalis', as described by Aristotle, and has been given a modern interpretation by Huiskes' question, namely: 'If bone is the answer, then what is the question?' (Huiskes, 2000). The question of function is all the more difficult with plants (and other living organisms) because of their multifunctionality and, especially in plant biomimetics, because the transfer of a functional principle and, thus, a desired function is sought. For example, Barthlott & Neinhuis (1997) (Fig. 2a). Micromorphological-anatomical and chemical investigations have deciphered the functional principle, which has been transferred to the facade paint Lotusan ® to achieve the self-cleaning function. However, unlike the biological model, the paint cannot fully restore the selfcleaning surface once it has been damaged.

IV. Biomimetics and sustainability
Because of the inspiratory flow from nature, biomimetic products seem to promise extraordinary qualities, such as a contribution to sustainability (von Gleich et al., 2010). However, the mission statement of sustainability is a human-made target agreement and not a natural concept, since evolutionary development is neither anthropocentric nor target-driven. Therefore, sustainability cannot be an automatic by-product of biomimetics . Similarly, in their analyses of the promises of biomimicry, MacKinnon et al. (2020) conclude that all sustainability claims can only be fulfilled if a special ethos and a respectful approach to nature complement the technological ambitions in practice. Qualitative and quantitative assessments on sustainability can best be made by comparing biomimetic and conventional products. Antony et al. (2016) carried out a comparative sustainability assessment of the biomimetic paint Lotusan ® and a conventional paint. Lotusan ® has been identified as a cost-effective and resourcesaving product, with both paints performing similarly well in all impact categories.

V. Closing remarks and future perspectives
Although the thematic fields have changed time and again, plants have been models for biomimetic products or methods from the very beginning of humankind. Recently, the functional morphology of plants has become key to biomimetic applications. An indication is the increasing numbers of special issues on biomimetics and the number of plant-based research papers therein (Fratzl et al., 2016;Gorb & Speck, 2017;Geitmann & Gril, 2018;Bushan, 2019aBushan, ,b, 2020Geitmann et al., 2019;Mazzolai et al., 2020) and the number of presentations at the Plant Biomechanics Conferences on 'applied biomechanics' and 'biomimetics' (Fig. S2). The presented examples of bioinspiration show that the boundary between the fields of biology and technology is becoming increasingly permeable. The higher the degree of permeability of the boundary between them, the more likely are bioinspired developments (cf. Neinhuis, 2017). Innovations, such as generative manufacturing or, in other words, technological construction as in biology from the small to the large, will increase the potential that the boundary will disappear completely in the future (Fig. 1f). We consider that the future of biomimetics involves the challenge of developing bioinspired products that will contribute to a more sustainable future than will conventional products.

Supporting Information
Additional Supporting Information may be found online in the Supporting Information section at the end of the article.  Please note: Wiley Blackwell are not responsible for the content or functionality of any Supporting Information supplied by the authors. Any queries (other than missing material) should be directed to the New Phytologist Central Office.