A Biomimetic Study of Long Shaft Cellulose Hooks after Arctium minus (Burdock) Paper 2(b)
Hooks associated with plant seed and fruit dispersal, with relatively long-shafts and short spans have been identified in five species and have already been the source of engineering design inspiration for George de Mestral and Velcro. However there are marked differences in the shape and functionality of natural hooks and the probabilistic fastener that he designed and developed. This paper continues the work of Part I and morphological study of the A. minus hook with an examination of the behaviour of A. minus under tensile load, the material behaviour and properties and the results are compared with results for four other species with similar hooks after the work by S. N. Gorb. It is concluded that there are four general indicators for product design apart from morphological variables already concluded by Gorb and these are flexible versus fixed bases to the shafts and degrees of resilience of the component material. The natural substrate properties are noted as being relevant but not necessarily governing.
Keywords: Fibre dimensions, tensile testing, fracture, composites, bending and axial loading, biological design indicators
The behaviour of the Artium minus hook under loading is studied here. The hook is composed of the bio-composite cellulose which is comprised of cellulose fibrils bound together in a matrix of hemi-cellulose and lignin. Full descriptions of the chemical composition and formation of these can be found in appropriate texts such as  and .
This paper forms parts two and three of the biomimetic process as described by Gorb , namely material study and mathematical analysis of loading. Note that Gorb includes duties for chemists in attachment structures that include secretions but this is not applicable in the case of burdock.
Part I of this study described the capturing of the morphology of the hook. Studying the functional ecology of the burdock hook must include its interaction and relationship with the substrate. In this paper this is limited to a cursory study since it will be relevant to the prototyping stage, further into this study. It was decided that the prototyping stage was the point at which this study would be performed in earnest since, as will be seen in the following papers, there is sufficient information already available from previous research.
This paper includes an investigation of the possible scaling effects associated with the burdock hook as per S N Gorb’s paper on the contact separation force of fruit burrs . The results are related to those of that paper and the methodology follows that of Gorb’s paper to a degree. The conclusions of this paper provide an indication of the direction which the design will take, following biological design indicators provided from A. minus, A. eupatoria, G. aperine and G. urbanum, the hooks that fractured in the test.
2 The substrate
In terms of the host substrate being fur or feathers, the qualities of these substrates have been studied elsewhere for other purposes. Table 1: the diameters of some common natural fibres.
- Natural fibre diameters 
|Type of hair||Diameter (microns)|
Hair is made of keratin. Keratins form a group of varied proteins which contain significant amounts of sulphur cross-linking and stabilizing in the material. It is found in horn, hair, hoof, feather, skin, claws etc. The types of keratin include mammalian, avian and others such as reptilian. 
In mammals, keratin occurs in hair, hoof and horn. Human hair is a composite consisting of a fibre/matrix mix. In a relaxed state the hair is mainly a-form and when heated and pulled straight it turns into a b-form. The a-form is the a-helix and the b-form is the anti-parallel b-sheet which results from pulling the a-helices beyond their yield point. Bird feathers are also made of keratins as is silk.
This can be related to the diameter of the hook, that is, the inner radius in order to seek design indicators of an optimum ratio. Such experimentation can be left until later in the product design but for the moment it should be mentioned that the inner diameter of the burdock hook, from outer tip to inner shaft surface, is approximately 250 microns.
The most important aspect to note with reference to the functionality of A. minus is not a critical geometrical relationship between the hook and a particular fibre but the fact that the hook accepts all fibre diameters for the purposes of mechanical interlock.
3 Tensile Testing of the A. minus Hook
To investigate the fracture force and mode of fracture of hooks from the plant genus Arctium minus or common burdock using an Instron tensile testing machine to observe any telling differences that could be observed from the conclusion of Gorb that the span of the hook was the significant factor in contact separation force by testing specimens of different radius of hook collected from burdock pods of varying diameters. Further, to observe the nature of fracture of the composite biomaterial and to use this information in developing a design for an attachment mechanism based upon the burdock hook and its functionality.
- “Natural hook-and-loop fasteners: Anatomy, Mechanical Properties and Attachment Force of the Jointed Hooks of the Galium aparine Fruit” E V Gorb, V L Popov, S N Gorb , and
- “Contact Separation Force of the Fruit Burrs in Four Plant Species Adapted to Dispersal by Mechanical Interlocking” E Gorb, S Gorb 
These two papers yield fundamental descriptions and conclusions upon which the following experiment is based. Their investigation into scaling effects in small hooks led to the following assertions: the four main attributes that influence burr performance are span, structure, size and material flexibility. All four species tested (were found to exhibit behaviour within the known bounds of cellulose performance. (E = 7 – 15GPa). The significant difference detected was an unforeseen weakness in strength displayed by C Lutetiana. This was associated with an increase in material flexibility; the hooks didn’t fracture, they flexed to release the loop and the hooks remained intact. This form of response is very similar to that of commercial Velcro (see Part III of this study).
The four main attributes described are repeated here:
- Structure: stomatal structures are smaller, rely upon the thickness of the cell wall and have stress concentrations at their base.
- Size: the longer the shaft length the greater the strength. This is probably due to a shaft diameter to length ratio, the longer the shaft the thicker the shaft.
- Span: the smaller the span of the hook the greater the strength due to a reduction in lever arm and hence bending moment.
- Flexibility: the greater the material flexibility the greater the chance of the test loop slipping from the hook.
Gorb suggests that it would be of interest to investigate the required force for detachment of the fruit from the stems but this was not considered relevant to this method for designing a biomimetic fastener.
- Specimens were collected from four separate burdock plants that grow behind the University of Bath accommodation blocks. The plants all stand in a line next to a sandy path that passes between the University grounds and the golf course.
- Note was maintained of the conditions of collection and the regions of the individual plants from which specimens were collected. These specimens were collected late in October 2003 and tested in December. It was observed that the plants themselves were brown and dry with the leafy vegetation of early season growth disappeared and the seedpod fully developed.
- Specimen hooks were collected in the form of whole fruits. The specimens were stored in paper packets until it was possible to conduct experiments upon them. (~30 days).
- It was judged that the effect of the delay between the collection and testing of the hooks would have little effect on the relative performance of the hooks and probably little effect on the absolute performance of the individual hooks given that they were collected in a naturally desiccated state and maintained in a dry condition until ready for testing, thereby preventing/inhibiting decomposition. Their desiccated state also made them ready for SEM work.
- Five individual fruit specimens (each consisting of an array of approximately 100 hooked bracts) were collected from each plant giving 20 specimens in total. A selection of these specimens was then tested.
- At the commencement of each test the burdock fruit was sectioned in half and one half labelled and stored. These are still available.
Each fruit was sectioned into halves under a dissecting microscope. One of these halves was returned to the specimen packet in case more hooks from the same specimen would be required. The other hemisphere of bracts/ovary/seeds was separated to “free up” the hooked bracts that surround the ovary.
Ten individual hooks were taken from the dispersed hemisphere. These were mounted in preparation for testing in the Instron machine by gluing each separate bract to a plastic mounting with 5mm of the bract shaft with its hook extended and exposed for interaction with a testing substrate (in this case a loop of silk thread as will be discussed). The extension was set at 1mm/sec using a 1N load cell.
Each specimen was mounted with 5mm +/- 0.3mm of shaft exposed, with the idea that all shaft lengths would be equal thereby reducing their influence upon the results. Gorb states that the shaft length is the principle main morphological variable influencing a hook’s strength. Thereafter, hook span and material flexibility are most important, the theory being that the larger the span the greater the lever arm of the bending moment and the stress at the shaft. In this case material composition is constant for all hooks.
- A rack of 5 hooks ready for testing
- Hook testing in the Instron Tensile tester. Arrow indicates looped thread.
Images were retained of all the stages of the experimentation.
- Fracture forces of burdock hooks [Height and Diameter of fruit refers to the entire fruit]. Specimens 1-3.
|Fracture Force (N)||Fracture Force (N)||Fracture Force (N)|
|Average fracture force||0.001004||0.000983333||0.00085375|
|Std dev (s)||0.031685959||0.003401055||0.000150867|
|Fruit Height (mm)||17.5||10||14|
|Fruit Diameter (mm)||23.5||15||14|
- Fracture forces of burdock hooks [Height and Diameter of fruit refers to the entire fruit] Specimens 4-6.
|Fracture Force (N)||Fracture Force (N)||Fracture Force (N)|
|Average fracture force||0.001163333||0.001168||0.00117875|
|Std dev (s)||0.002073291||0.000250516||0.000108428|
Figure 3 below shows the detachment/fracture force of each set of specimen hooks. The mean value of these results for each specimen is plotted versus the diameter of the fruit.
- Average fracture force of hooks of specimens 1-6
- The contact separation of the burrs from Gorb et al 
Figure 4: shows the results of Gorb et al’s experiments. Note how the results of C. lutetiana show the lowest contact separation force as these hooks flexed due to material resilience. Comparing these with the force results below shows that the results for A.minus fall between those of A. eupatoria and G. urbanum but significantly higher than the other species with a flexible base, G. aperine.
|Mean Hook Fracture Force (N)||Fruit height (mm)||Fruit diameter (mm)|
The SEM images of the fractured hooks in Figure 5: overleaf clearly show the fibrous nature of the hook material. The fracture surface indicates that the inner fibres failed in tension. Thereafter the outer fibres too failed in tension. The composite nature of the material is demonstrated and noting how the fracture surface fractures unevenly, there is substantial fibre “pull-out”. From Prof J F V Vincent’s notes on the mode of fracture of fibrous composites from  the fibre “pull-out” indicates that the fibre/matrix interface of the plant material consisting of cellulose microfibrils, hemi-cellulose and lignin is tightly bound. It can be seen from Figure 5 that all 4 specimens (taken to be typical examples) experienced failure on the inner curvature of the hook as would be expected for a hook of material experiencing a bending moment with the inner fibres under tension while the external fibres are in a state of relative tension about a point of rotation. The surface is typical of a fibrous composite break in bending. All hooks fractured at the region of the join between hook and shaft which is the region of the entire hook structure (both shaft and arced tip) that experiences the stress when the hook is placed in tension.
- SEM’s showing sample fracture surfaces of cellulose microfibrils
The specimen fruit size ranged from 14mm to 26mm in diameter. It was reasonably assumed that the sizes of hooks increased proportionally from fruit to fruit, including shaft length and span.
With reference to Table 4: (the graph of fracture forces) it can be seen that the hook fracture forces are all of the same order of magnitude but that there is a levelling of the slope in the region of the diameter equalling 20mm.
The separation force levels out at 1.2 mN which can be taken to indicate the ultimate tensile strength of the cellulose microfibrils and the point at which the crack accelerates across the fracture plane. More on this follows in the next section.
All hooks fractured in the region just beneath or at the commencement of curvature. This is in line with bending theory since the material at this point will experience the highest bending moment and the maximum distortion, particularly at the innermost fibres which will be in tension. These fibres will experience the highest strain as the hook tries to straighten under loading. The outermost fibres will be in compression as the hook distorts and “straightens” under loading. Once the inner fibres have failed the full load is then transferred to the outer fibres which immediately fail in tension under the significantly higher stress.
- Scheme of morphological burr variables from Gorb et al 
- Images of burr separation for each of the four species from Gorb et al  and lastly an image of a burdock hook prepared for testing with silk thread.
With reference to Figure 7: the specimen sequence is, left to right, A. Eupatoria, C. Lutetiana, G. aperine, G. urbanum, A. minus. Note the difference in diameter of wire used by Gorb and thread. Both the wire loop and the silk thread represent an artificial substrate, replacing natural fibre. Silk thread is a composite of natural silk which is much finer than fur fibres. The wire loop appears much finer than a natural fibre and the question should be asked if it contributed to severing the hook tips.
The analysis that follows derives from undergraduate engineering structural analysis. Note that although cellulose is a biocomposite, the density of the fibres in the fibre/matrix composite is such that for the purposes of analysis the hook material shall be treated as an anisotropic solid. The basic morphology of the hook shall follow the sketch in Figure 6. Dimensions for the hook are taken from the SEM below. An SEM of a fractured hook has been placed alongside.
- An SEM of an minus hook reproduced from Part I and an SEM of a fractured hook which appears again later in the Results.
Let the hook be placed under tension. The stresses in the material will comprise two components due to the tensile loading:
- Free Body Diagram and stress diagrams for the bending stress and axial stress characteristic of a hook under tensile load from Fenner 
From Part I it is noted that the A. minus hook does not taper in diameter from the top of the shaft. Instead there is an increase in material on the shoulder of the hook before it tapers to a point. This must have an influence on the hook’s behaviour in tension, increasing its resistance to flexing, increasing its attachment to its host and its disposition to fracture.
The analysis of a hook under loading is completely presented in Fenner .
Vincent  presents standard figures for the elastic modulus of cellulose as 7-15 Gpa and notes that for biomaterials the Poisson ratio is generally taken to 0.5 (though not always).
By using these figures as a maximum and minimum value and calculating the stress due the loading it should be possible to evaluate the percentage strain during the test. All dimensions are taken from Figure 8. Calculations are based upon the sketches in Figure 9.
This calculation shall be based upon the average fracture force of specimen 3 i. e.
f = 0.001168 N
E = elastic modulus = s/e = stress/strain (1)
st = tensile stress = force/area = f/A (2)
where the area is the cross-section of the hook.
A = (p *d**2)/4 (3)
Where d = 200 x 10-6
L = lever arm = d/2 + span/2 (4)
Span = 100 microns, therefore
L = 200 microns
st = (1.17 x 10-3 x 4)/(p x (120 x 10-6)2) = 1.035MPa
sbm = (100 x 10-6 x 200 x 10-6 x 1.17 x 10-3 x 4)/(p x (1202 x 10-6)2)
= 2.069 x 10-3 Pa
stotal = 1.035MPa
Now by substituting each of the range values of E = (7-15GPa) for cellulose we find emn and emax.
emax = 0.000148, emin = 0.000069
These results suggest that:
- Since the strains are so low, there must be some other reason for failure.
- The bending moment has a negligible impact upon the failure in direct stress.
If we consider shear stress, ss = Fs/A
Where A is the angled shear plane at angle q and Fs is the shear component of the applied load, then
Fcosq /Asecq = ts (5)
Let q = 30o
Then ts = ((1.17 x 10-3)cos q)/((p x d**2) x secq/4)
If G = E/(2 x (1 + u)) (6)
Then G = E/3 = (2.33Mpa, 7.5Mpa)
And g, the shear strain, where g = t/G (7)
= (13.7, 4.23)
This suggests that the hooks fail in shear due to the bending moment.
This experiment confirms that the separation force of a natural hooked structure is indirectly dependent upon the span or radius of a hook and directly dependent upon the component material’s resistance to shear.
It could be assumed in mechanical design of a hook that the smaller the span of the hook the higher the separation force since this would reduce the tensile stress due to the bending moment. But in composite biomaterials this is not the full story. The bending moment does not add substantially to the direct stress the hook experiences. The true weakness can be found in the cellulose microfibril’s low resistance to failure in shear.
From Vincent  biomaterials have two types of natural resistance to crack retardation, the Cook-Gordon model where a weak matrix/fibre interface intercepts the crack propagation and absorbs energy of crack propagation and the second is a toughening coating on the exterior of a material. In this test which was performed on an Instron tensile tester which applies load through displacement, the load is not removed or eased after the first crack appears. Loading continues at the same rate (1 mm/sec in this case). This means that there is no chance for any natural resistance to appear as the hook is steadily ripped apart.
There can be reasonable argument put that using a Poisson’s ratio of 0.5 is not accurate and this may be true. However even so, the results for strain (e) are very low. From observation of the SEM’s of fracture there isn’t any sign of delamination in compression which means that the matrix fibril interface remained intact.
This experiment helps illustrate the types of properties that shall be important in the specification of a product. Further it demonstrates (as a biological indicator) that it would be better to design a single degree of freedom hook from a composite than a multiple degree of freedom hook which would result in a decrease in strength. It must be born in mind that all the hooks in this experiment as well as in Gorb’s will demonstrate energy efficiency and therefore material and stress optimization in their structure.
- Vincent J. F. V., Structural Biomaterials, The Macmillan Press, 1982
- Devlin R. M., Witham F. H., Plant Physiology, Fourth Ed., Devlin and Witham, PWS, 1983
- Gorb S. N., Miniature attachment systems: Exploring biological design principles. Design and Nature, DN02/40799, 2002
- Gorb E, Gorb S, Contact Separation Force of the Fruit Burrs in Four Plant Species Adapted to Dispersal by Mechanical Interlocking. Plant Physiology and Biochemistry, 40, pp. 373-381, 2002
- Stamburg G., Wilson D., Veterinary Medicine http://www.llamapaedia.com/wool/
- Popov E. V., Popov V. L., Gorb S. N., Natural hook-and-loop fasteners: anatomy, mechanical properties, and attachment force of the jointed hooks of the Galium aparine fruit. Design and Nature Review Paper DN02/40800 2002
- Fenner R. T., Mechanics of Solids, Blackwell Scientific Publications, pp. 296-297, 1993