A Biomimetic Study of Long Shaft Cellulose Hooks after Arctium minus (Burdock) Part III

Bruce Saunders

Abstract

Keywords:

1  Introduction

It is necessary to consolidate information before proceeding with the design. The morphology of the A. minus hook has been accurately recorded and its performance under tension has been tested and compared with those of four other species []. A. minus is supposed to be the biological inspiration behind Velcro [] and it is interesting to compare their relative functionalities. It will become apparent that functionally, the Velcro hook resembles that of C. lutetiana more than it resembles the hook of A. minus. This shall lead to product description based upon long-shaft cellulose hooks and the opening elements of the design process for a product closely based upon the shape, functionality and material of these hooks.

In considering the hooks of A. minus, C. lutetiana, A. eupatoria, G aperine, and G. urbanum the hooks of each of these plant species is associated with plant dispersal, for attaching the plant fruit to passing hosts but each has a different hook arrangement in terms of number of hooks per fruit and their arrangement on the fruit. Gorb’s purpose in studying C. lutetiana, A. eupatoria, G aperine, and G. urbanum [] was to find an optimum hook (or burr) morphology, investigate scale effects of the burrs per fruit and to assess the contact force of a single burr compared to the mass of the fruit. By adding a study of A. minus to his work and concentrating on burr morphology and material properties and assessing the structural information available it will be shown that the biological indicators do indeed supply information that can lead to the generation of a product or a family of products that is different from conventional Velcro, by following a biomimetic process. (Note: At no stage in this work has a patent database been consulted. This was a purposeful omission so as not to influence the biomimetic process.)

In all five species the burrs in their various formations and numbers form probabilistic fasteners. By definition from Nachtigall [] a probablistic fastener is a random hooking mechanism that is a releasable attachment mechanism by one structure, i.e. there is no single matching structure required for attachment to take place. This definition does not specify that the structure should be part of a field of structures nor that interaction between component structures is a necessary part of attachment. Considering Gorb’s work on frictional parabolic fasteners [] his model specifically includes the interaction of neighbouring elements as contributing directly and not indirectly, to the attachment. All the hooks of the five species in this paper are a part of fields of structures of different numbers but the hooks do not interact to increase their individual attachment force. They all act individually and their collective action serves to arithmetically increase the overall attachment of the fruit to the host.

Further, it is stated by Gorb [] that he has an interest in measuring the scaling effects of the detachment force of the fruit from their supporting structure on the parent plant. If one considers that the burrs have a direct purpose of hooking the fruit to a host then it would seem that with respect to his study of morphological variables and their respective influence on burr strength [] there are finite possible responses when a hook comes into contact with a host. They are:

1. Fruit detachment from the parent plant.
2. Hook flexure if fruit detachment does not take place, to release the host and keep the hook intact for the next host.
3. Removal of host fibres.

Any other response such as hook fracture and shaft fracture would result from the fruit being held in place on the parent plant and would render the hook useless for its intended purpose which would be contrary to an evolutionary strategy.

2  Hook structure

Three of the species (C. lutetiana, G. aperine, A. eupatoria) are the weakest in tension and they originate from trichomal structures. From Devlin [] trichome is a collective noun for all types of outgrowths supported by the cell wall of the epidermal layer. The epidermis is the outermost layer of cells in a plant and its functions include manufacturing the structural material of the plant. A trichome is a plant hair and can be glandular and non-glandular, cellular, multi-cellular, branched or unbranched. Of these three species, G. aperine exhibits a multi-degree of freedom due to, from Gorb [], a hollow base. The other two species derive from the surface of the mericarp.

Of the other species, A. minus  and G. urbanum, their hooks originate from the bract and carpel of the fruit and exhibit respectively the strongest contact separation forces. Both have a single degree of freedom due to their origination from a flattened structure.

From this information it is possible to derive space charts of biological hook design criteria for cellulose hooks:

High Strength

Low Strength

Trichome                                               Sepal

Structure

High Strength

Low Strength

Small                                                      Large

Size

High Strength

Low Strength

Fixed base                             Single                                     Multiple

Degrees of Freedom

High Strength

Low Strength

Low                                                                        High

Elastic Modulus

All of these are based upon hooks made of cellulose. Introducing materials suitable for manufacture with their own properties will produce different relationships.

3  Functionality

3.1   Plant hooks

The following is compiled from both the research of Parts I and II and from the papers of Gorb et al [] [].

1. In the plant kingdom, with regards to plant growth and evolution, only energy efficiency can be assumed with regards to structure. All structures are governed by the same basic physical and chemical laws.  This implies a direct link between material composition, morphology and function but does not necessarily indicate a best overall solution to a prescribed problem from an engineering perspective since engineers have a wide variety of materials at their disposal.
2. The tensile testing upon Arctium minus confirmed that S N Gorb’s conclusion with regards to hook strength, that shaft strength and then hook radius was of primary importance morphologically speaking were true to a degree but that the material resistance to shear induced by bending was more important than the influence of bending moment due to the length of the lever arm.
3. It was noted that functionally burdock hooks are single use only and that the originating bracts, from which the hooks form act as a single degree of freedom hinges thereby aiding attachment.
4. It was noted that the diameter range of known natural host hair fell between 20 and 100 microns in diameter, all consisting of the material a-keratin.
5. It was observed that burdock hooks have a radius or curvature of between 50 and 150 microns and a thickness of approximately 200 microns and that cellulose microfibril alignment is all parallel to the direction of the hook.
6. It was observed that unlike Velcro, burdock hooks have a pointed tip and their hooks are thin enough in silhouette to combine a hooking function with an action of piercing the fibres.
7. It was noted that hooks originating from trichomes (plant hairs) appear to be weaker that hooks originating from carpels or bracts. This could be due to the fact that trichomes are simpler structures and less developed.

3.2   Velcro

As a product, Velcro is purported to derive from burdock. It is of interest therefore to make a comparison between the two before attempting to develop a further product biomimetically from these plant hooks.

1. It was noted that the nylon from which Velcro is manufactured is flexible and resilient enough to withstand multiple attachments and re-attachments.  The artificial substrate however can be damaged over time.
2. It was observed Velcro hooks which are assembled in parallel fields which is similar to the spherical fields of both the A. minus and the G. urbanum.
3. It was observed that confocal microscopy, although memory intensive, was a viable means of non-destructive indirect measurement of a micron-sized cellulose hook with natural fluorescent properties.  Further it is surmised that the product of a confocal microscope, a stack of .tif images, could be converted directly for virtual reality applications, rapid prototyping devices and could have application in the field of producing nano- and micro-structures.

4  Design brief

Unlike conventional design briefs where a required function is specified with parameters to place constraints on the design, here it is the shape and functionality that is specified for which a suitable material and application is sought.

4.1   Shape

‎Figure 1 shows the burdock hook shape that shall be used in the design. It shall be taken as prescribed. This image is repeated from Part I. This shape shall be central to the full design.

• 3-d reconstruction from SolidWorks of a burdock hook and shaft

4.2   Functionality and structural description

4.2.1    Hook

In considering the range of attachment types shown in the five species considered, they indicate that a certain range of hooks could be considered (see ‎Figure 1 to ‎Figure 4) varying in structure, flexibility, size and strength. If structure and size are considered to be “given” constraints, flexibility and strength are material and manufacturing properties. Because of the asymptotic approach to the design all possibilities can be explored and confirmed or eliminated as the design progresses. Considering the reproduction of a hook as shown in ‎Figure 5 the following functions can be defined:

1. To hook and to flex to release substrate or not to flex and not release.
2. To pierce such that the hook can be inserted with a forward action like a barbed spike or simply to thread between a fibrous substrate.
3. To flex in a single plane to aid attachment through a flexible base, not to flex in any plane or to flex in multiple planes.

4.3   Shaft

The structure of the burdock hook indicates shows that the shaft emerges from a flattened supporting bract. The burdock bract itself is rectangular with the hook emerging from one of the narrow edges. This bract has its own permanent attachment to the fruit pedicle at the base. Replicating this bract opens a number of possibilities in terms of hook configurations. See Section ‎4.2.3 below.

A flexible base could be produced by mimicking the hook of the G. aperine fruit. This would rely upon introducing a variable material thickness in the shaft to allow buckling in different directions.

A solid inflexible base is the third possibility and will produce increased strength and directionality, perhaps at the cost of efficiency of attachment.

4.3.1    Substrate

The substrate shall be defined by testing for suitability and attachment strength and shall be dependent upon the finished size, shape and material of the hook. The natural substrate for cellulose hooks is fibrous. Similarly this could be replicated for a product but this is not a necessity. It will depend upon the selected material and the abilities and application of the finished design.

For instance, in considering biomedical applications such as sutures it would seem that a barbed spike is a better solution for piercing flesh than a piercing hook but this may not necessarily be the case since the success of such an implement must depend upon the amount of trauma induced, the recovery and the behaviour in situ post recovery. These effects cannot be assumed.

4.3.2    Hook field structure

It has been noted that hooks in nature are assembled in different configurations and numbers. Gorb compared the mass of the fruit with the contact separation force of single hooks in order to assess the hook performance for each species and the number of hooks required to support the fruit which could be viewed as a measure of design efficiency.

With the design progressing with a development of a modular hook, a hook with supporting “bract”, the opportunity exists to experiment with:

1. Field configurations, densities and numbers.
2. Bract shapes i.e. square, rectangular, circular, octagonal etc.
3. Bract attachment mechanisms for both attaching bracts to each other to form composite fields as well as for attachment to a structure needing an attachment mechanism.
4. Bract shapes also offer the opportunity to manufacture the hooks in flattened rows.

In fact modularising the hooks appears to offer many permutations which eventually will have to be modified during the process of material selection and manufacturing process selection and refined by application.

4.3.3    Scaling Effects

The ability to reproduce scaling effects shall be constrained by the mode of manufacture and material selection. It is clear that scaling effects are maximized when a material or structure is acting at its physical limits as occurs in optimized and very small structures. Since a burdock hook is made of cellulose, scaling effects combine with material properties to produce the resultant effect. It follows therefore that an artificial material, stronger than cellulose, will demonstrate reduced scaling effects.

4.4   Product Development

The image overleaf shows the result of extending the digitized burdock hook through a lofted feature into a flange similar to the flattened bract from which the natural bract originates. This image represents a modular hook from which the product design can be developed.

A Biomimetic Study of Long Shaft Cellulose Hooks after Arctium minus (Burdock) Part II

Bruce Saunders

Abstract

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

1  Introduction

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 [‎1] and [‎2].

This paper forms parts two and three of the biomimetic process as described by Gorb [‎3], 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 [‎4]. 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 [‎5]

Type of hair	Diameter (microns)
Human	90-100
Llama	20-40
Fine wool	19.5
Mohair	25-45
Merino wool	12-20

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. [‎1]

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

3.1   Aim

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.

     This experiment draws from the methods and is compared with the results of the following two papers:

1. “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 [‎6], and
2. “Contact Separation Force of the Fruit Burrs in Four Plant Species Adapted to Dispersal by Mechanical Interlocking” E Gorb, S Gorb [‎4]

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:

1. Structure: stomatal structures are smaller, rely upon the thickness of the cell wall and have stress concentrations at their base.
2. 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.
3. Span: the smaller the span of the hook the greater the strength due to a reduction in lever arm and hence bending moment.
4. 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.

3.2   Method and Apparatus

1. 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.
2. 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.
3. 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).
4. 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.
5. 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.
6. At the commencement of each test the burdock fruit was sectioned in half and one half labelled and stored. These are still available.

3.3   Specimen Preparation

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.

3.4   Results

• Fracture forces of burdock hooks [Height and Diameter of fruit refers to the entire fruit]. Specimens 1-3.

Specimen No	1		2		3
		Fracture Force (N)		Fracture Force (N)		Fracture Force (N)
	1	0.00101	1	0.00114	1	0.00057
	2	0.00104	2	0.00121	2	0.00108
	3	0.00107	3	0.00099	3	0.0011
	4	0.00103	4	0.00095	4	0.00083
	5	0.00087	5	0.00098	5	0.00092
			6	0.00085	6	0.00091
			7	0.0009	7	0.00092
			8	0.00093	8	0.00107
			9	0.0009	9	0.00115
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.

Specimen No	4		5		6
		Fracture Force (N)		Fracture Force (N)		Fracture Force (N)
	1	0.00135	1	0.00059	1	0.00139
	2	0.00093	2	0.0011	2	0.00114
	3	0.00112	3	0.0012	3	0.00112
	4	0.00124	4	0.00088	4	0.00106
	5	0.00114	5	0.00109	5	0.00105
	6	0.001	6	0.00118	6	0.00131
	7	0.00086	7	0.00127	7	0.00127
	8	0.00113			8	0.00109
					9	0.0012
Average fracture force		0.001163333		0.001168		0.00117875
Std dev (s)		0.002073291		0.000250516		0.000108428
Height (mm)		16		17		17
Diameter(mm)		26		25		23

‎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 [‎6]

‎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.

• Specimens 1 – 6 mean hook fracture forces and dimensions of whole burdock fruit

 

Mean Hook Fracture Force (N)	Fruit height (mm)	Fruit diameter (mm)
0.001163	16	26
0.001168	17	25
0.001168	17.5	23.5
0.001179	17	23
0.000983	10	15
0.000854	14	14

3.4.1    Images of fracture

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 [‎1] 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

3.4.2    Discussion

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.

3.5   Analysis

• Scheme of morphological burr variables from Gorb et al [‎6]

• Images of burr separation for each of the four species from Gorb et al [‎6] 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 [‎7]

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 [‎7].

Vincent [‎1] 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)

s_t = 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

s_t = (1.17 x 10^-3 x 4)/(p x (120 x 10^-6)²) = 1.035MPa

s_bm = (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

s_total = 1.035MPa

Now by substituting each of the range values of E = (7-15GPa) for cellulose we find e_mn and e_max.

e_max = 0.000148, e_min = 0.000069

These results suggest that:

1. Since the strains are so low, there must be some other reason for failure.
2. The bending moment has a negligible impact upon the failure in direct stress.

If we consider shear stress, s_s = F_s/A

Where A is the angled shear plane at angle q and F_s is the shear component of the applied load, then

Fcosq /Asecq = t_s                                                                                                                         (5)

Let q = 30^o

Then t_s =  ((1.17 x 10^-3)cos q)/((p  x d**2) x secq/4)

= 32MPa

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.

3.5.1    Conclusion

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 [‎1] 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.

4  References

1. Vincent J. F. V., Structural Biomaterials, The Macmillan Press, 1982
2. Devlin R. M., Witham F. H., Plant Physiology, Fourth Ed., Devlin and Witham, PWS, 1983
3. Gorb S. N., Miniature attachment systems: Exploring biological design principles. Design and Nature, DN02/40799, 2002

1. 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
2. Stamburg G., Wilson D., Veterinary Medicine http://www.llamapaedia.com/wool/
3. 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
4. Fenner R. T., Mechanics of Solids, Blackwell Scientific Publications, pp. 296-297, 1993

Part I: The Biomimetic study of Cellulose Hooks: Burdock (Arctium minus) OR How to make a cellulose hook that’s small and efficient..