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Plant Biomechanics Group Hanns-Christof Spatz |
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Prof.
Dr. Hanns-Christof Spatz |
Selected
Publications:
7) H.-CH. Spatz and Donald M. Crothers (1969)
8) D.M. Crothers and H.-CH. Spatz (1971)
10) H.-CH. Spatz and T.A. Trautner (1970)
25) D. Menne and H.-CH. Spatz (1977)
30) C. Hernandez de Salomon and H.-CH. Spatz (1983)
45) A. Aszodi, U. Müller, P. Friedrich, and H.-CH. Spatz (1991): Signal Convergence on Protein Kinase A as a Molecular Correlate of Learning. Proc. Natl. Acad. Sci., USA, 88, 5382-5386
46) H.-CH. Spatz (1991): Circulation, Metabolic Rate and Body Size in Mammals. Journal of Comparative Physiology B, 161, 231-236
47) H.-CH. Spatz, Ch. Boomgarden and Th. Speck (1993)
64) Spatz, H.-CH., F. Brüchert, A. Emanns, and T. Speck (1997): Biomechanics of Arundo donax. Phil. Trans. Roy. Soc. B 352, 1-10
80) Spatz, H.-CH. and F. Brüchert (2000)
92) Spatz, H.-CH. and O. Speck (2002)
93) Köhler, L. and H.-CH. Spatz (2002): Micromechanics of plant tissues beyond the linear elastic range. Planta, 215, 33-40
99) Speck, O. and H.-CH. Spatz (2004): Damped oscillations of the giant reed Arundo donax. Am J Bot 91, 789-796
100) Spatz, H.-CH. and A. Emanns (2004): The mechanical role of the endodermis in Equisetum plant stems. Am J Bot 91, 1936-1938
103) Niklas, K. J. and H.-CH. Spatz (2004): Growth and hydraulic (not mechanical) constraints govern the scaling of tree height and mass. Proceedings of the National Academy of Sciences (USA) 101: 15 661 - 15 663
108) Niklas, K. J., H.-CH. Spatz and J. Vincent (2006): Plant Biomechanics: An Overview and Perspective. Am J Bot 93, 1369-1378
110) Spatz, H.-CH., F. Brüchert and J. Pfisterer (2007b): Multiple resonance damping or how do Trees Escape Dangerously Large Oscillations? Am J Bot 94, 1603 - 1611
Books:
- G. Hertting and H.-CH. Spatz, ed.:
Modulation of Synaptic Transmission and Plasticity in Nervous Systems.
NATO ASI Series, Springer Verlag 1988.
- Spatz, H.-CH. and Th. Speck: Plant
Biomechanics 2000: Proceedings of the 3rd Plant Biomechanics Conference
Freiburg-Badenweiler, Thieme Verlag, Stuttgart (2000)
Current Research in Plant Biomechanics
Research Goals:
We try to understand how plants withstand static and dynamic mechanical loads. Stability is described on the structural level, on the level of the plant's tissues, and on the molecular level.
Projects
Mechanical resistance of hollow plant stems to bending loads
Stability of trees against wind loads
Oscillations and their damping in plant stems
Publications 2000 - 2007 in Plant Biomechanics
Publications 1990-99 in Plant Biomechanics
Mechanical resistance of hollow plant stems to bending loads
Hollow structures such as the stalks of cereals have the advantage that stiffness against bending can be achieved at relatively low biological cost. However, such structures are endangered by local buckling. Despite of the economical importance, theoretical approaches describing the phenomenon of local buckling are rare. In engineering sciences most approaches apply only to very thin walled cylindrical shells of isotropic material.
We developed a theoretical approach to calculate critical bending moments for local buckling of hollow cylinders of anisotropic and nonhomogeneous material. The theory was extended to incorporate the stabilizing influence of nodal thickenings and of an inner lining of turgescent parenchymatous tissue. The description of the ovalization of thick walled rings takes into account the local equilibrium between bending and shear deformations.
Several testing methods were developed to measure the mechanical properties of hollow plant stems. Moduli of elasticity in the longitudinal direction, ovalization of the cross-section and critical compressive strains could be measured simultaneously. Local buckling was characterized by measuring the critical curvature and the critical bending moments just prior to the collapse of the structure. Moduli of elasticity in tangential direction and critical strains were determined by transverse compression of segments of the hollow stems. For the Giant Reed Arundo donax shear moduli of the parenchyma could also be determined. This way all the input parameter for the theory of local buckling became available. As a critical test for our numerical theory the mode of failure in Arundo donax, namely longitudinal splitting due to ovalization, could be predicted quantitatively.
Arundo donax owes its remarkable stability to a graded lignification of the parenchyma. Another way of encountering the danger of local buckling is realized in Equisetum giganteum, where the structure is stabilized by an inner lining of turgescent parenchyma. Nevertheless, above a height of 2.5 meters isolated stems are mechanically unstable. Consequently, the growth habit is that of a typical semi-self-supporter, where stems support each other by interlacing with their side branches.
As in Equisetum giganteum, the hollow stem of Equisetum hyemale owes the mechanical stability of the internodes to an outer ring of strengthening tissue (hypodermal sterome) which provides stiffness and strength in the longitudinal direction. In contrast to hollow-stemmed grasses, the hypodermal sterome consists of living cells. The compound inner lining of the overwintering aerial stem of Equisetum hyemale includes a continuous inner and outer endodermis layer of vital thick-walled cells that have slightly lignified Casparian thickenings. The two endodermis layers provide an inner tension and compression bracing which lends resistance to local buckling.
Stability of trees against wind loads
Wind loads on trees were calculated as distributed loads depending on the tree's geometry and the particular wind profile. By measuring the bending stiffness of the branches "controlled flexibility" could be taken into account and the degree of streamlining at high wind velocities be assessed. The resulting bending moments on individual trees were compared to the critical bending moments for green wood as determined experimentally on fresh samples from the same tree on an Instron Testing Machine. For steady winds the results allow to estimate the speeds at which stem breakage is likely to occur.
Oscillations and their damping in plant stems
Important mechanical properties of plant stems can be assessed by measuring the frequency of oscillations and their damping. We studied oscillations of Arundo donax stems in the field either with or without leaves by video analysis and frame by frame evaluation. The data show that the oscillations can be described as bending vibrations. Oscillations and their damping was also investigated for plant stems of Cyperus alternifolius, Equisetum hyemale, Equisetum fluviatile, Thamnocalamus spathaceus, Stipa gigantea, and Juncus effusus. With the exception of Thamnocalamus spathaceus damping of the isolated plant stems without side organs, leaves or inflorescence is remarkably effective. Our experiments support the hypothesis that embedding stiff vascular bundles in a more compliant parenchymatic matrix provides the structural basis for dissipation of mechanical energy in the plant stem.
Upper and lower estimates of the oscillation frequencies for upright tapered stems, non-negligible mass and an additional load (mass) attached at one point along the stem, can be derived from solutions of the differential equation for bending oscillations, available for certain limiting cases (Mathematica 4.0, Wolfram Research Inc.). A special case is encountered for zero frequency, where the differential equation becomes identical to Greenhill's equation for Euler buckling.
Upon dynamic wind loads trees may get into large sways and even fail in a resonance catastrophe. Oscillation damping is essential for the survival of a tree. We studied oscillations of a 5m high Douglas fir and of its stem without branches. Damping was 7 times more effective in the tree than in the stem. By recording the amplitude of the oscillation and computing the relative amplitude as a function of height, as well as measuring the orientation, the height above ground and the geometrical properties of all 99 branches, we derived at an estimate of the aerodynamic damping. Under the assumption (to be disproved!) that the branches do move in line and in phase with the stem, aerodynamic damping was even less effective than damping within the wood of the stem. Thus "Structural Damping" must account for the larger part of the tree's capability to reduce the amplitude of oscillations.
Structural damping is a phenomenon occurring frequently in gusty winds, when branches do not sway in line with the stem but rather perform independent relative movements. In order to understand the underlying principle we built a simple physical model consisting of a main axis and two side arms. We observed that the structure performed quite complex movements if the frequency was close to the eigenfrequency of the side arms. In this mode of damping, which we call "Multiple Resonance Damping", energy is transferred from the main axis to the side arms and damping is more efficient.
In analogy we presumed that the eigenfrequency of the branches is close to the natural frequency of the entire tree. By determining the taper of the primary branches, their modulus of elasticity and the mass distribution including secondary and higher order branches we could calculate their eigenfrequencies. The data corroborate our presumption for all larger branches. We, therefore, conclude that the remarkably high damping in the tree is mainly due to a distribution of mechanical energy between stem and side-branches, where it is dissipated more effectively.
The difference in the damping of Cyperus alternifolius stems with and without leaves can be attributed to the aerodynamic resistance of the leaves. In contrast structural damping plays an important role in Stipa gigantea with its inflorescence and in Arundo donax with leaves. This mode of damping can be described as "Mass Damping".
Publications 2000 - 2007 in Plant Biomechanics
Beismann, H., Wilhelmi, H., Baillères, H., Spatz, H.-CH., Bogenrieder, A. and T. Speck (2000): Brittleness of twig bases in the genus Salix - fracture mechanics and ecological relevance. J. Exp. Bot., 51, 617 - 633.
Köhler, L., Speck, T. and H.-CH. Spatz (2000): Micromechanics and anatomical changes during early ontogeny of two lianescent Aristolochia species. Planta, 210, 691 -700.
Köhler, L. (2000): Biomechanische Eigenschaften und ihr Einfluß auf das mechanische Verhalten von Aristolochia macrophylla und Aristolochia brasiliensis. BIONA report 14, 148 - 152.
Niklas, K.J. and H.-CH. Spatz (2000): Wind-induced stresses in cherry trees: Evidence against the hypothesis of constant stress levels. Trees, Structure and Function, 14, 230 - 237.
Spatz, H.-CH. and F. Brüchert (2000): Basic Biomechanics of Self-Supporting Plants: Wind loads and gravitational loads on a Norway spruce tree. Forest Ecology and Management, 135, 33 - 44.
Speck, O., Speck, T. and H.-CH. Spatz (2000): Arundo donax as a damped harmonic oscillator. BIONA report 14, 143 - 147.
Ennos, A.R., Spatz, H.-CH. and T. Speck (2000): The Functional Morphology of the Petioles of the Banana Musa textilis. J. Exp. Bot., 51, 2085 - 2093.
Spatz, H.-CH. (2000): Greenhill's formula for the critical Euler buckling length revisited. In: Proceedings of the 3rd Plant Biomechanics Conference, (H.-CH. Spatz and T. Speck, eds.), Thieme-Verlag, Stuttgart, 30 - 37.
Speck, O. and H.-CH. Spatz (2000): Oscillation and damping behaviour of the giant reed Arundo donax. Proceedings of the 3rd Plant Biomechanics Conference (H.-CH. Spatz and T. Speck (eds.), Thieme-Verlag, Stuttgart, 39 - 44.
Niklas, K.J. and H.-CH. Spatz (2000): Response to Klaus Mattheck's letter. Trees, 15, 64 - 65.
Speck, T. and H.-CH Spatz (2001): Transkription oder Translation: Pflanzen als Ideengeber für neue Materialien und technische Leichtbaustrukturen. In: BIONIK - Ökologische Technik nach dem Vorbild der Natur ? (A. v. Gleich, Hrsg.) B.G. Teubner Verlag, Stuttgart, 2. Auflage.
Spatz, H.-CH. (2001): Sicherheitsfaktoren in der Biomechanik von Bäumen. Jahrbuch der Baumpflege 2001. Bernhard Thalacker Verlag, Braunschweig, 164 - 170.
Spatz, H.-CH. (2001): Sicherheitsfaktoren in der Biomechanik von Bäumen (Kurzfassung). Landschaftsarchtektur 31, Heft 2, 29 - 32.
Speck, T., O. Speck and H.-CH. Spatz (2001): Pflanzen als "Ideengeber" für die Technik. BIONA report 15, 187 - 202.
Spatz, H.-CH. and J. Zebrowski (2001): Oscillation Frequencies of Plant Stems with Apical Loads. Planta, 214, 215 - 219.
Spatz, H.-CH. and O. Speck (2002): Oscillation frequencies of tapered plant stems. Am J Bot 89, 1 - 11
Köhler, L. and H.-CH. Spatz (2002): Micromechanics of plant tissues beyond the linear elastic range. Planta, 215, 33 - 40
Speck, T., Rowe,N., Civeyrel,L., Claßen-Bockhoff, R., Neinhuis, C. and Spatz, H.-Ch. (2003): The potential of plant biomechanics in functional biology and systematics. In: T. Stuessey, F. Hörandl & V. Mayer (eds.), Deep Morphology: Toward a Renaissance of Morphology in Plant Systematics. Koeltz, Königstein. Chapter 12, pp.: 241 - 271.
Brüchert, F., Spatz, H.-CH, and O. Speck (2003): Oscillations of plant stems and their damping: theory and experiments. Phil. Trans. R. Soc., London B 358, 1487 - 1492.
Speck, O. and H.-CH. Spatz (2003): Mechanical properties of the rhizome of Arundo donax L. Plant Biology 5, 661 - 669.
Pfisterer J.A., Spatz H:-CH.., Erforth D. and H. Marten (2003): Untersuchungen zur Biegebruchfestigkeit von Astgabeln der Hasel (Corylus avellana L.). In: Dujesiefken D., Kockerbeck P. (Hrsg.), Jahrbuch der Baumpflege 2003; Braunschweig (Thalacker Verlag), 255 - 268.
Spatz, H.-CH. (2003): Kronensicherung und Auffangsicherung: ein Kommentar zur ZTV - Baumpflege, 2001, Tabelle 1 des Anhangs. Stadt und Grün 52, 43 - 45.
Speck, O. and H.-CH. Spatz (2004): Damped oscillations of the giant reed Arundo donax. Am J Bot 91, 789 - 796.
Spatz, H.-CH. and A. Emanns (2004): The mechanical role of the endodermis in Equisetum plant stems. Am J Bot 91, 1936 - 1938.
Bargel, H., H.-CH. Spatz, T. Speck and C. Neinhuis (2004): Two dimensional tension tests in plant biomechanics - sweet cherry fruit skin as a model system. PLANT BIOLOGY 6, 432 - 439.
Spatz, H.-CH., Emanns A. and O. Speck (2004): The structural basis of oscillation damping in plant stems. Journal of Bionics Engineering 1, 149 - 158.
Niklas, K. J. and H.-C. Spatz. 2004. Growth and hydraulic (not mechanical) constraints govern the scaling of tree height and mass. Proceedings of the National Academy of Sciences (USA) 101, 15661 - 15 663.
Niklas, K. J. and H.-CH. Spatz (2006): Allometric Theory and the Mechanical Stability of Large Trees: Proof and Conjecture. Am J Bot 93, 824 - 828.
Spatz, H.-CH., F. Brüchert and J. Pfisterer (2006): How do Trees Escape Dangerously Large Oscillations? In: Proceedings of the 5th Plant Biomechanics Conference, (L. Salmen, ed.), p. 275 - 280.
Pfisterer, J. and H.-CH. Spatz (2006): Biomechanical behaviour of branch junctions. In: Proceedings of the 5th Plant Biomechanics Conference, (L. Salmen, ed.), p. 61 - 66.
Niklas, K. J., H.-CH. Spatz and J. Vincent (2006): Plant Biomechanics: An Overview and Perspective. Am J Bot. 93, 1369 - 1378.
Spatz, H.-CH., F. Brüchert and J. Pfisterer (2007a): Wie reagieren Bäume auf dynamische Windlasten oder wie können Bäume einer Resonanzkatastrophe entgehen? Jahrbuch der Baumpflege 2007; Braunschweig (Thalacker Verlag), 260 - 269.
Spatz, H.-CH., F. Brüchert and J. Pfisterer (2007b): Multiple resonance damping or how do Trees Escape Dangerously Large Oscillations? Am J Bot 94, 1603 - 1611.
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18/ 10/
07.....Responsible: H.-Ch. Spatz