Sept. 10. Materials for force transferSkeletal constitutents: composites: matrix & fibres: mesoglea (pliant), mollusc shells, clockwise, counterclockwise, shell as locomotory organ?, insect cuticle, calcite (trilobite eyes), wood (carpenters and framing), bone, tendon, chitin, apodemes, collagen and crossed-fibre helical connective tissue arrays. Viscoelastic materials: mucus and cilia and slugs sliding on snot. Sclerotization and stridulation; resilin, abductin as antagonists; allometry and geometric morphometrics, size and scaling.

Bad plan to try to stick to this original syllabus – need to be able to change content.Picture shows-lectures and lab preambles define course content – not the syllabus. I will try to update the syllabus as to what actually happened in the lectures as we proceed.

Announcement: As I finish the projected part of lectures, the ‘picture shows’, I will post them, after editing, on the website as ‘Picture Shows’. The old ‘picture shows’ from a previous incarnation will remain there for a bit. But the new ones will be added as they occur within a few days of each lecture. These picture shows will not include all that was said in lecture.

I also plan to add material as ‘essays’ from time to time. There is one there on the tentorium at the moment that you should read and another coming shortly on Materials.

First assigned readings

Denny Mark 1980. The role of gastropod pedal mucus in locomotion. Nature 285: 160-161.“The yield-heal characteristics of this mucus are ideally suited to the locomotion of A. columbianus. During locomotion 12 to 17 muscular waves are present on the slug’s foot...”Ritchie Robert O. 2011. The conflicts between strength and toughness. Nature Materials 10: 817-822. See Website essay under ‘Essays source paper’.Vincent Julian F.V. & Wegst Ulrike G.K. 2004. Design and mechanical properties of insect cuticle. Arthropod Structure and Development 33: 187-199.

You are not ‘responsible’ for understanding everything in these papers: read to clarify and add to the points made in lecture.

• FIRST EFFORT FULCRUM LOAD• SECOND FULCRUM LOAD EFFORT• THIRD FULCRUM EFFORT LOAD

• For more background on levers see Vogel 2nd ed. Chapter 24, p. 473.

Three classes of lever are named on the basis of sequencing effort, load, fulcrum.

Skeletons both exoskeletons and endoskeletons, move forces about. They translocate them, they leverage them. What are the functions of levers? To amplify forces, to set forces against one another: antagonize.

Scallop adductor is a 2nd class lever

The load of the shell is taken as acting through the centroid of the bivalve, this being closer to the hinge than the muscle; the effort of the adductor muscle ‘lifts’ this load.Abductin at the hinge is a

material not a muscle, a rubbery antagonist of the adductor muscle; it acts elastically, storing energy in distortion when the adductor contracts, to return it at a later time.Abductin as inner and outer ligament: one acts as a 2nd class other as 1st .

Leverage involves a force causing body-part rotation: the force from shortening adductor muscles pulls on the adductor apodeme inserted on the mandible base; this rotates the whole structure through a short arc toward the midline (fat blue arrow)..

To decide where the load should be considered to act, you need the point of balance, i.e., the centroid or centre of gravity.

[Force can be represented as a vector,showing magnitude and direction.]

When “a force has a line of action lying to one side of an axis of rotation... we call the shortest, or perpendicular, distance between the force’s line of action and the axis, the ‘moment arm’ or the ‘lever arm’ of the force” (Vogel 2nd). A moment of force is the product of the force magnitude and this lever-arm distance to the line of action.

Force moment

“Levers are practical applications of ...moments” Vogel

Force-advantage levers vs distance- (or) speed-advantage levers

• Vogel advocates using the term force advantage instead of mechanical advantage, because mechanical advantage can be misleading: a muscle often actually works at a leverage ‘disadvantage’.

• Force advantage is the ratio by which the applied force is multiplied (amplified) by the lever.

• Where force is more important than speed in the life of an animal evolution will want a force-advantage lever, one where the effort arm is longer than the load arm, so maximizing the moment of the effort – the force-in or effort moment.

• Distance advantage is force advantage’s reciprocal: the ratio of the distance the load moves to the distance moved by the effort. [“Distance advantage must correspond to ‘speed advantage’ – if an action takes a given time, then going farther means going faster”.]

• When speed and distance are more important than force you will want a longer load arm than effort arm giving a relatively greater moment to the load.

Force advantage: ratio by which the effort is multiplied by the lever; moment arm of effort divided by moment arm of the load.

Distance advantage: ratio of the distance moved by the load relative tothat moved by the effort.

Speed advantage: ratio of the speed at which the load moves relative to that of the effort.

Force and distance/speed advantage are inversely related: good force advantage goes with a relatively poor distance/speed advantage; good distance/speed advantage with a relatively poor force advantage.

Redrawn Fig. 24.1 of Vogel

Both up and down insect-wing movements are a (first class) distance-increasing lever – a lever with good speed advantage, and a relatively poor force advantage; there is a very short force arm, the moment arm of the effort is divided by the much larger moment arm of the load – the centre of gravity of the wing being much farther from the fulcrum.

“A muscle... is relativelygood at producing forceand relatively bad at gettingshorter. ...any engine that gets only 20 % shorter will have to operate with a substantial distance advantage to move a long limb [wing] through an angle that may approach 180 degrees. For that good distance advantage it will necessarily suffer a poor force advantage because the product of the two must be unity...” (Vogel 2nd , p. 475)

Class 3 lever for both up and downstrokes of the

wings

As with the insect wing, the bird wing is a distance (& speed)-increasing lever. Distance advantage will be >1: put in a small distance get out a large.Distance advantage: ratio of the distance moved by the load (weight of the wing) relative to that moved by the effort (contracting muscle) is much greater than 1.The effort arm in a flying bird is not longer than the load arm, so not maximizing the moment of the effort.

Paired antagonistic muscles, blade

apodemes and a dicondylic joint in the flexion (depression)

and extension (levation)

of the jumping, (metathoracic) leg of

the locust

Pinnate muscle via apodeme: more powerful than orthogonal (direct) fibres

To avoid having to draw, and only use words for organ description: see this wonderful old book of terminology for entomologists.

• Torre-Bueno, J.R. A Glossary of Entomology. Brooklyn Entomological Society• acclivous – rising gently• acetabulum – cavity into which an appendage is articulated• acicular – needle-shaped (e.g. spine of Chestnut is acicular)• aculeate – armed with short sharp points (e.g., burr of burrdock is not aculeate)• acuminate – tapering to a long point• adnate – adjoining (e.g., radius and subcosta are adnate)• alate – winged etc. Takes a while to get to ‘unguis’: one of the claws at the end of

the tarsus, plural ungues• unguiform – shaped like a claw; unguiflexor – muscle flexing the ungues of an

insect; unguifer – the median dorsal process or sclerite on the end of the tarsus to which the pretarsal claws are articulated etc. Unguiflexor lets me illustrate a rope apodeme, one specialized to convey tensile stress as well as the fact that not all antagonists are other muscles.

Locust rope apodeme and unguiflexor muscles

unguiform – shaped like a claw; unguiflexor – muscle flexing the ungues of an insect; unguifer – the median dorsal process or sclerite on the end of the tarsus to which the pretarsal claws are articulated etc. Unguiflexor lets me illustrate a rope apodeme, one specialized to convey tensile stress as well as the fact that not all antagonists are other muscles.

ungue

Apodemes can also be designed for tension

Like the scallop the antagonist of the unguiflexor is elastic material

Arthropod cuticle: a hierarchical composite materialsource: Vincent J.F.V. & Wegst U.G.K. 2004. Design and mechanical properties of insect cuticle. Arthropod

Structure and Development 33: 187-199. (see Assigned reading)

• Many animal materials are composites: a material made by combining two other materials: soft composites are made of a “rubbery matrix reinforced by fibres… a material that is composed of two quite different materials… can have better properties than either material on its own” (Ennos 2012).

• My canoe is made of a composite material, isolated glass fibres embedded in a continuous resin matrix. Cuticle, the integument of all animals in the phylum Arthropoda, functions as exoskeleton and is a composite material.

• Arthropod cuticle consists “…of arrangements of highly crystalline nanofibres embedded in a matrix of protein, polyphenols and water, with small amounts of lipid.”

• It is “praeternaturally (surpassing the ordinary) multifunctional” (Vincent 2004).• “The cuticle… not only supports the insect, it gives it its shape, means of

locomotion, waterproofing and a range of localised mechanical specialisations such as high compliance, adhesion, wear resistance and diffusion control. It can also serve as a major barrier to parasitism and disease.”

Ennos Roland 2012. Solid Biomechanics. Princeton Univ. Press, Princeton, Oxford.

Chitin is a polysaccharide akin to cellulose. One chitin nanofibre (see the 19 chains in Vincent’s Fig. 1) is 3 nm in diameter, 0.3 micrometeres long. “The fibrous composite cuticle derives its properties from its components, which can be varied in orientation... and volume fraction to produce the wide range of mechanical properties: chitin nanofibres, type of protein, water content and degree of cross-linking of the protein [sclerotization], lipid, metal ions, calcium carbonate.” Fig 1. Section of chitin nanofibre looking along the chitin.

Matrix: imagine aspider web of interconnecting silk in 3 dimensions.

Praeternaturally functional

• .”..the insect cuticle also has to form sensors, joints, wear-resistant mandibles, devices for elastic energy storage, effective attachment systems...” (Vincent & Wegst 2004)

• Cuticle composition varies topographically in an animal’s skeleton – varies in thickness, toughness, elasticity – so it can bend effectively at a joint, or as a blade apodeme give broad surface to muscle fibre origins, act as a brace in a tentorium, or function like a pulling rope, resisting tension created by unguitractor muscle; it can be very thin in gills to allow the gas exchange of aquatic insects, or become thick and tanned and resist compression in a crushing mandible. [Sclerotization and tanning are chemical processes that toughen cuticle by creating stable cross-linkages within the composite.]

• The important point is that adaptive form (the theme of 325) extends down through hierarchially organized material structure showing adaptation throughout. Not only is cuticle shaped for crushing food at the organ level (e.g., a grasshopper mandible) but the cuticle’s microstructure – the structure of “crystalline chitin nanofibres embedded in a matrix of protein, polyphenols and water” (Vincent & Wegt 2004) has evolved to e.g., offset fracture: exoskeleton substance is adapted to make toughness where it is needed.

• “The tensile and shear stiffnesses and strengths… are much larger when fibres are alligned parallel to the applied load.”

• The cuticle is secreted by a single layer of epidermal cells that covers the entire surface of the insect, extending into the tracheal system, fore- and hind gut, and part of the genital system. …It can be as thin as 1 micrometre in the hindgut and over gills [where transport matters] and as thick as 200 micrometres “(wing-covers, of large beetles) [where mechanical protection strength and toughness are needed].

• The cuticle “…frequently is multilayered with a plywood-like structure “ • Plywood analogy: “If high stiffness in more than one direction is required , as is

the case in most parts of the cuticle, ‘laminating unidirectional layers in a variety of directions produces the desired properties.”

• (Vincent & Wegst 2004)

This mollusc, a gastropod (snail), carries about its shell as a refugium, a protective retreat. The microstructureof the shell has evolved be able to resist the mechanical forces directed at it by predators.

The shell is an important extracellular feature (organ) of animals in the phylum Mollusca.

Assigned reading: see R.O. Ritchie The conflicts between strength and toughness. 325 website Essay source paper

• “Mollusc shells are also another fine example of nature’s design of damage-tolerant materials. ...these materials have a ‘brick-and-mortar structure; the ‘bricks’ are ~0.5 µm thick, 5-10 µm wide, platelets of the mineral aragonite (a polymorph of calcium carbonate) that comprise some 95% of the structure, separated by an organic biopolymer mortar in-between (Fig. 5a).”

See further comments on the importance of this paper in the section of the website headed Essays source papers

the platelets (I think) are missing theirmatrix in this scanning electron micrograph

Wikkipedia on ‘nacre’

• Nacre is composed of hexagonal platelets of aragonite (a form of calcium carbonate) 10–20 µm wide and 0.5 µm thick arranged in a continuous parallel lamina. These layers are separated by sheets of organic matrix composed of elastic biopolymers (such as chitin, lustrin and silk-like proteins). This mixture of brittle platelets and the thin layers of elastic biopolymers makes the material strong and resilient, with a Young's modulus of 70 GPa (when dry). Strength and resilience are also likely to be due to adhesion by the "brickwork" arrangement of the platelets, which inhibits transverse crack propagation. This design at multiple length sizes greatly increases its toughness, making it almost as strong as silicon.

Young’s modulus (values from Gordon 1978) is the ratio of stress to strain (stress/strain) and measures stiffness. Cuticle of a ‘pregnant’* locust 0.2; rubber 7; human tendon 600; wood along the grain 14000; iron 210000.

*Locusts in a reproductive state are not said to be ‘pregnant’ by any entomologist.