Plant Biomechanics Group Hanns-Christof Spatz

Prof. Dr. Hanns-Christof Spatz Institute for Biology III Albert-Ludwigs-University Schaenzlestrasse 1 D-79104 Freiburg i.Br. Tel: +49-761-203-2710 FAX: +49-761-203-2745 E-mail: spatz@biologie.uni-freiburg.de

Selected Publications:

Books:

Hertting, G. 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 (2000): Plant Biomechanics 2000: Proceedings of the 3rd Plant Biomechanics Conference Freiburg-Badenweiler, Thieme Verlag, Stuttgart

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

 

• Stability of trees against wind loads

   

• Mechanical resistance of hollow plant stems to bending loads

   

• Oscillations and their damping in plant stems

   

• Lignin content, stem anatomy and mechanical behaviour of Aristolochia macrophylla

   

• Micromechanics of plant tissues beyond the linear-elastic range

   


 

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Publications 2000 - 2004 in Plant Biomechanics

Publications 1990-99 in Plant Biomechanics

Plants investigated || Methods applied


 

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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.

 

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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.

 

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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.

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 ( Mathematica 4.0, Wolfram Research Inc.) for certain limiting cases. A special case is encountered for zero frequency, where the differential equation becomes identical to Greenhill's equation for Euler buckling.

Oscillations and their damping was investigated for plant stems of Cyperus alternifolius L., Equisetum hyemale L., Equisetum fluviatile L., Thamnocalamus spathaceus (FRANCH.) SODERSTR., Stipa gigantea LINK, and Juncus effusus L. 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. 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.

 

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Lignin content, stem anatomy and mechanical behaviour of Aristolochia macrophylla


The elastic properties of the axes of Aristolochia macrophylla have been described by T. Speck 1994 (Bending stability of plant stems: ontogenetical, ecological, and phylogenetical aspects. Biomimetics 2, 109-128). As typical for lianas the stiffness shows a decrease with older ontogenetic stages.

The analysis was now extended to younger ontogenetic stages still in the phase of elongation growth. We examined mechanical properties such as Young's modulus, critical strains and viscoelastic behaviour by longitudinal tension and the shear modulus by torsion around the longitudinal axis. To relate these mechanical properties to the underlying structures the tissue distribution was quantitatively analysed in stem cross-sections, the amount of cell wall material was determined, the cellulose microfibril orientation was measured by X-ray scattering and the lignin content of the samples was quantified by thioglycolic acid derivatization and subsequent spectroscopic analysis. (Köhler et al, 2000).

During the development of the plant a characteristic variation of the mechanical stiffness can be found: starting from around 0.01 GPa in the youngest ontogenetic stages the modulus of elasticity increases to around 3 GPa in the fully differentiated axes and finely decreases again in the older ontogenetic stages to around 0.3 GPa. This correlates with the stem anatomy and also with the lignin content. Together with the effect of chemical lignin extraction on intact tissue samples and the changes in mechanical properties during ontogeny in non-lignified plants this sheds light on the specific role of the lignin for the overall mechanical behaviour.

 

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Micromechanics of plant tissues beyond the linear-elastic range


The most common type of stress-strain relation of plant tissues strained in tension is a linear-elastic range with no yield and sudden total failure. Most kinds of dryed wood fall into this category as well as fibres from Cannabis sativa, Phormium tenax and Musa textilis and various plant cuticles. In contrast, other strengthening tissues of plants show a typical biphasic stress-strain relation in tension: two linear ranges with a transition point in between and a lesser slope of the second section compared to the first. This is reported for different fibres such as Agave americana or Cocos nucifera, for wood from Juniperus virginiana, for the strengthening tissues of Fontinalis antipyretrica, Equisetum hyemale, Aristolochia species and for some plant cuticles. This characteristic biphasic behaviour is also known for other bio-materials such as the locusts intersegmental membrane or tendon collagen. While for tendons the structural basis of the complex mechanical behaviour is well investigated, the only comprehensive work dealing with this problem on plant tissues was published at the beginning of the last century (Sonntag P (1909): Die Duktilen Pflanzenfasern, der Bau ihrer mechanischen Zellen und die etwaige Ursache der Duktilität. Flora 99, 203-259). More recent literature is limited to only mentioning this phenomenon.

From the side of the materials sciences certain two-phase composite materials such as fibrous glass reinforced plastics are described having comparable mechanical behaviour and corresponding structural elements. The decrease in the slope of the stress-strain curve beyond the transition point is explained here with yield of the matrix and slippage of the fibres past each other.
We investigated the relation between cell wall structure and the resulting mechanical characteristics of different plant tissues. Special attention was paid to the mechanical behaviour beyond the linear-elastic range, the underlying micromechanical processes and the fracture characteristics. The previously proposed model of reorientation and slippage of the cellulose microfibrils in the cell wall [H.-CH. Spatz et al. (1999) J Exp Biol 202:3269-3272) was supported and is here refined, using measurements of the changes in microfibrillar angle during straining. Our model explains the widespread phenomenon of stress-strain curves with two linear portions of different slope and sheds light on the micromechanical processes involved in viscoelasticity and plastic yield. We also analysed the velocity dependence of viscoelasticity under the perspective of the Kelvin model, resolving the measured viscoelasticity into functions of a velocity-dependent and a velocity-independent friction. The influence of lignin on the above-mentioned mechanical properties was examined by chemical lignin extraction from tissues of Aristolochia macrophylla Lam. and by the use of transgenic plants of Arabidopsis thaliana (L.) Heynh. with reduced lignin content. Additionally, the influence of extraction of hemicelluloses on the mechanical properties was investigated as well as a cell wall mutant of Arabidopsis with an altered configuration of the cellulose microfibrils.

 

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02/12/04.....Responsible: H.-Ch. Spatz