The mollusk, the arch and conjugate shearing

I’ve written repeatedly on this blog about nature’s masons.  Nature is the ultimate inspiration for design;  evolution showcases many masonry techniques.

Mollusks have recently been investigated by two researchers at MIT, graduate student Ling Li and Professor Christine Ortiz.  Their research findings were published in the journal ‘Nature Materials’ (March, 2014) and focused on the mollusk Placuna placenta. 

This mollusk’s shell exhibits very tough qualities (resistant to crack propagation) while simultaneously remaining optically transparent.  When subject to extreme focused stress -such as may be encountered by its predators- the calcite material of Placuna placenta’s shell demonstrated very efficient energy dissipation and the ability to localize deformation, limiting damage to the area directly impacted and preventing crack propagation.

The mollusk’s shell is comprised of around 99% calcite and around 1% organic material which bind the calcite crystals together.  This is somewhat similar to the sharp defensive spikes found in sea urchins (as discussed here) which are also made primarily of calcite with small amount of organic binder material present.  Pure calcite (without organic binder) is a brittle crystalline material which easily cracks.

The mechanism wherein the type of deformation in Placuna placenta shell occurs was studied by using an indentation apparatus consisting of a diamond tip which is forced into the mollusk shell.  The resulting damage to the indent region was then visually recorded using electron microscopy and diffraction techniques to characterize the resulting damage.

This research cleverly showed that the deformation (or strain) of the mollusk shell was a crystallographic ‘twinning’ response to the applied stress.  Crystal twinning occurs when two separate crystals share some of the same crystal lattice points in a symmetrical manner. The result is an intergrowth of two separate crystals in a variety of specific configurations. A twin boundary or composition surface separates the two crystals.

Part of the crystal shifts its position in a predictable way, leaving two regions with the same orientation as before, but with one portion shifted relative to the other. This twinning process occurs all around the stressed region, helping to form a kind of boundary that keeps the damage from spreading outward (preventing crack propagation).

This twinning mechanism provides for conjugate shearing.   The conjugate shearing mechanism has significance in terms of a toughened structure and is better than a conventional masonry arch structural response to an applied stress of voussoirs forming hinges.

Conjugate shearing was initially employed by geologists as a term to describe shear fractures in rocks subject to compressive stress.  The context and scale of this geologic feature have kept it from being analyzed, utilized or realized in the context of microscopic analysis or in the context of masonry design and modular structural systems.   Similarly, it is apparent that biologists and engineers have failed to fully appreciate the conjugate shearing mechanism demonstrated by the Placuna placenta’s calcite shell structure in response to applied stresses such as the indentation tests done by researchers at MIT.

The force required to cause conjugate shearing to occur (in an architectural arch or in a mollusk shell) is much higher than the force required to create a hinging mechanism as occurs in a conventional masonry arch comprised of wedge-shaped voussoirs.  For example, Thor’s hero shrew’s spine is configured in such a manner that it is disposed to conjugate shearing instead of creating a hinging mechanism which leads to buckling and collapse of the spine.  An adult human can stand upon and be supported by the tiny Thor’s hero shrew’s spine without breaking the poor animal’s back.  Conversely, a common shrew does not have the interlocking triangular design of Thor’s hero shrew’s vertebrae; its spine would buckle and collapse in the hinging mechanism of a conventional masonry arch if an adult human stood on top of it: the back would simply and easily be broken (poor regular shrew).

The calcite shell of Placuna placenta and its unique crystallographic twinning response to applied stress is another of Nature’s exemplars of exquisite design which incorporates the structural response of conjugate shearing to create a toughened structure which will blunt and stop crack propagation in an otherwise brittle material. 

Architecture and Plate Tectonics

In its third episode ("When Knowledge Conquered Fear") the recent version of “Cosmos” by Neil deGrasse Tyson featured an interesting segment involving Robert Hooke, Edmond Halley, Isaac Newton and the discovery of gravity.  Tyson’s treatment of this subject neglected to mention Hooke’s discovery of the funicular or catenary form, which is a unique insight dependent on gravity.   Hooke’s revelation anticipates and incorporates gravity. 

Hooke revealed his discovery describing how a masonry arch works in a teasing anagram with a succinct introduction:   "The true Mathematical and Mechanical form of all Manner of Arches for building, with the true butment necessary to each of them. A Problem which no Architectonic writer hath yet attempted, much less performed. abcccddeeeeefggiiiiiiiillmmmmnnnnnooprrsssttttttuuuuuuuux."

Hooke did not provide a translation of this anagram during his lifetime.  It was finally revealed by his executor in 1705:  "Ut pendet continuum flexile, sic stabit contiguum rigidum inversum--As hangs a flexible cable, so inverted, stand the touching pieces of an arch."  This insight has been the essential summary of Masonry Science and arch design since its 1705 revelation.

Hooke’s use of the word “Architectonic” in the preface to his anagram is interesting if we consider its etymology and related words and phrases.  Architectonic (adj.)  1:   of, relating to, or according with the principles of architecture. 2:  having an organized and unified structure that suggests an architectural design.  From “Arch” (arch) + “tectonic” (building). 

“Plate tectonics” is a geological term used to describe the movement of rigid sections of the earth’s crust around the planet.  If an arch is considered as completely as possible, it is a sphere.  Plate tectonics may be viewed as a dynamic planetary architectonic.  Plates are divided by three types of boundaries: divergent (crust is created), subduction (crust is destroyed) and shear boundaries (crust slides against crust).

Tectonic plates slide against each other in the manner of conjugate shearing.  If the creation and destruction of crust are neglected, one is left with a series of plates which will conjugate shear around a spherical surface.  How can one design plates which will conjugate shear around a spherical surface?

Gratis deGrasse Tyson, for neglecting Hooke’s flexible cable hanging under gravity and allowing me to ramble on about arches, architects, architectonics and plate tectonics.  

Thor's Hero Shrew and masonry design

I have written a few times on this blog about masonry in nature, as evidenced by several species of animals, including seahorses.  A couple years ago a new species of shrew was discovered in the Democratic Republic of Congo, whose spine exhibits incredible strength and toughness.  “Thor’s Hero Shrew” is worth taking a look at from the perspective of interlocking masonry design.

As discussed in this article, “Scientists at Chicago's Field Museum and international collaborators have described a new species of Hero Shrew – the mammal with the most bizarre lower spine on Earth. The interlocking vertebrae of the Hero Shrew render the spine four to five times more robust relative to body mass, a condition not found in any other mammal. The spine has been an enigma to evolutionary biologists, with no known adaptive significance.

This new species of Hero Shrew, named Scutisorex thori, possesses features that may represent intermediate character states between the only other known Hero Shrew species (Scutisorex somereni), and other shrews. In addition, a novel hypothesis for the function of the animal's expanded lower spine has been proposed. The study will be published July 24, 2013 edition of Biology Letters.

First discovered in 1910, the Hero Shrew's most notable feature was not revealed for another seven years, when a specimen was dissected to reveal the most peculiar backbone of any mammal. The remarkable spine of the Hero Shrew is unique among mammals, in that the lower vertebrae have multiple lateral processes that interlock with the processes of neighboring vertebra. The arrangement, along with surrounding musculature, affords the animal extraordinary strength, so much so that the Hero Shrew has traditionally been worn as a talisman.

"This shrew first came to light when explorers came to the eastern part of the Democratic Republic of Congo," said Bill Stanley, Director of Collections and zoologist at the Field Museum. "The explorers watched in amazement as a full-grown man stood on the back of the Hero Shrew, and the animal walked away, unharmed."

Until now, there have been no other species of this bizarre shrew. The new species described in this study represents a possible intermediate between the original Hero Shrew and other shrews, since is possesses an interlocking spine, but with fewer lower vertebrae and lateral processes than the first Hero Shrew species.

"You and I have five lumbar vertebrae," said Stanley. "And so do most other mammals, but the Hero Shrew at least 10. Scutisorex thori has eight vertebrae, and fewer lateral processes than the original species."

The specimen of the new Hero Shrew species was collected in the lowland forest near the Tshuapa River in the Democratic Republic of Congo. Based on the observations of one of the co-authors on the study, the authors present a novel hypothesis for the functional significance of the spine of Scutisorex thori; they suggest that these shrews position themselves between the trunk and leaf bases of Palms, and use their unique spine to exert force and gain access to concentrated sources of beetle larvae that are otherwise protected from predation. The same adaptation may allow these animals to lift logs or rocks to access invertebrates – a food resource that remains unavailable to many other mammals.

The specimen of Scutisorex thori now residing at The Field Museum is a holotype, meaning that it will be the standard for identifying other members of the species. The new species is named in honor of Thorvald "Thor" Holmes, Jr. of the Humboldt State University Vertebrate Museum, at the suggestion of Bill Stanley, who did his graduate work there. The suggested common name is "Thor's Hero Shrew", appropriately invoking Thor, the god of strength in Norse mythology.

"The Age of Discovery is not over," said Stanley. "In fact, discoveries such as these happen in natural history collections, like the ones that we have at The Field Museum. In addition, hypotheses such as the one that we've generated concerning the functional significance of the Hero Shrew's spine fuel the scientific machine. We can't wait to see the results of further scientific studies that test the ideas presented in this article."

As Wikipedia states, “The structure of Thor's hero shrew's cranium and vertebrae suggest that it may be descended from an evolutionary intermediate between the hero shrew and other shrews. Its existence may help explain the evolution of the hero shrew which, Stanley explains, has historically been cited as an excellent example of punctuated equilibrium, a theory that holds that species sometimes evolve very rapidly in short periods of time after long periods of stability. The existence of an intermediate species hints at a more gradual or incremental evolution for the hero shrew's extreme specialization.”

It appears to me that Thor’s hero shrew utilizes an interlocking masonry-like arrangement to achieve the incredibly high spinal strength it possesses.  The ability to sagitally flex its spine would seem to indicate conjugate shearing between lumbar vertebrae, similar to the seahorse tail strength mechanism.

Nature is the Grand Master of design.  Thor’s hero shrew is an exemplar of masonry technique used to achieve high strength and toughness.  Its discovery is perhaps an omen of punctuated equilibrium in the evolution of masonry as used by man.

Seahorse's tail strength and conjugate shearing

Earlier I wrote a blog entry here on Nature’s masons.  I tried to describe how nature offers inspired design solutions from different animals which use properties of masonry to their advantage, including: foraminifera, radiolaria, coral, sea anemones, turtles, tortoises and more.   Today I want to attempt to describe a masonry feature used by another animal, the seahorse.

Seahorse’s tails have a bony structure which withstands extreme pressures without breaking.  The bones of the tail form a roughly square limb in cross section.  There are sets of four corner bones to this tail structure which run its length.  These four bones are triangular, and are disposed to conjugate shearing.

 

I have discussed conjugate shearing and how masonry structures can benefit from conjugate shearing as a means to relieve stress(applied force) through strain (movement).   This is just how a seahorse’s tail reacts to any threatening stress: it deforms via conjugate shearing instead of breaking.  When the stress is relieved the triangular bones return to their original position, tail intact.

A paper recently published in Acta Biomaterialia (Highly deformable bones: unusual deformation mechanisms of seahorse armor   Michael M. Porter et al, published Fe. 26, 2013) describes the elegant design of seahorse tails, including the bony structure and how it allows for conjugate shearing, making the tail very strong, robust and tough.

The design of a seahorse tail has inspired human designers to employ the same concept in robotic armor design, as discussed in several recent articles.  Nature is always an inspiration for good design.

A new engineering model for a new block

Contemporary engineering analysis of masonry arches provides a model which is not adequate for analysis of the masonry system I’ve been describing on this blog (dual inverse mirror plane, or ‘dimp’).  A new model is required to analyze this triangular interlocking system, which I shall attempt to describe.

The currently accepted engineering model makes three assumptions about masonry arches.   (1)  Masonry units have no tensile strength (2) Masonry units are infinitely strong in compression (3) Blocks (or voussoirs) never slide against each other.  An arch modeled on these 3 assumptions is then viewed in cross section, and a catenary thrust force line is imposed on the wall thickness of the arch.  If the thrust force line touches or exits the wall thickness, then a hinge is formed at that point (between two adjacent blocks or voussoirs) and the arch will buckle and collapse.  If a large force is applied to the arch, the thrust force line will eventually touch or exit the inside (intrados) or outside (extrados) of the masonry arch, and failure will result in a hinging mechanism which causes the arch to buckle and collapse.

The dimp design can employ a tensile element, like a wire or cable within the wall thickness of the block.  This feature gives the arch some tensile strength.  When a large force is applied to this arch, the tensile action of the cable or wire counters this force and keeps the imaginary thrust force line more toward the center of the arch thickness.  In addition to this tensile containment, another feature of the dimp comes in to play.

A large force applied to a dimp arch will first be contained by some of the tensile web, woven as great circle arcs.  Instead of hinges forming when the thrust force line touches the intrados or the extrados, conjugate shearing occurs (as described here).  Control joints allow block faces to slide against each other; they are actually designed to.  This deformation is a strain (movement) resulting from excessive stress (applied force).  The strain relieves the stress, and when the applied force is removed, the structure returns to its original state.  The forces which restore a deformed arch are from gravity and the tensile elements.  There is of course a limit to an applied force, beyond which a dimp arch will collapse, but it is greater than that of a conventional arch constructed from voussoirs of the same thickness.  

Thus the currently accepted method of engineering analysis for masonry arches does not appear to work for the dimp design.  First, an arch made of dimp blocks has tensile strength.  Second, the blocks move (slide) against each other.  Finally, instead of a hinging mechanism there is a conjugate shearing mechanism between blocks.  It is a whole different model.

I am currently working toward a computer model to reflect this different engineering analysis.   I hope to have it available to post here eventually.