Friday, September 9, 2016

The Biomechanics of Solids and Fluids: The Physics of Life

This summer a review article about biomechanics by David Alexander appeared in the European Journal of Physics: “The Biomechanics of Solids and Fluids: The Physics of Life” (Volume 37, Article 053011, 2016). It serves as an excellent supplement for much of the material in Chapter 1 (Mechanics) in Intermediate Physics for Medicine and Biology. It describes the biomechanics of solids (elasticity) and fluids (fluid mechanics).
"Biomechanics borrows and extends engineering techniques to study the mechanical properties of organisms and their environments. Like physicists and engineers, biomechanics researchers tend to specialize on either fluids or solids (but some do both). For solid materials, the stress–strain curve reveals such useful information as various moduli, ultimate strength, extensibility, and work of fracture. Few biological materials are linearly elastic so modified elastic moduli are defined. Although biological materials tend to be less stiff than engineered materials, biomaterials tend to be tougher due to their anisotropy and high extensibility. Biological beams are usually hollow cylinders; particularly in plants, beams and columns tend to have high twist-to-bend ratios. Air and water are the dominant biological fluids. Fluids generate both viscous and pressure drag (normalized as drag coefficients) and the Reynolds number (Re) gives their relative importance. The no-slip conditions leads to velocity gradients (‘ boundary layers’) on surfaces and parabolic flow profiles in tubes. Rather than rigidly resisting drag in external flows, many plants and sessile animals reconfigure to reduce drag as speed increases. Living in velocity gradients can be beneficial for attachment but challenging for capturing particulate food. Lift produced by airfoils and hydrofoils is used to produce thrust by all flying animals and many swimming ones, and is usually optimal at higher Re. At low Re, most swimmers use drag-based mechanisms. A few swimmers use jetting for rapid escape despite its energetic inefficiency. At low Re, suspension feeding depends on mechanisms other than direct sieving because thick boundary layers reduce effective porosity. Most biomaterials exhibit a combination of solid and fluid properties, i.e., viscoelasticity. Even rigid biomaterials exhibit creep over many days, whereas pliant biomaterials may exhibit creep over hours or minutes. Instead of rigid materials, many organisms use tensile fibers wound around pressurized cavities (hydrostats) for rigid support; the winding angle of helical fibers greatly affects hydrostat properties. Biomechanics researchers have gone beyond borrowing from engineers and adopted or developed a variety of new approaches— e.g., laser speckle interferometry, optical correlation, and computer-driven physical models— that are better-suited to biological situations.
One of my favorite parts of the review are the references. Alexander cites many of his own publications, including his book Nature's Flyers: Birds, Insects, and the Biomechanics of Flight. For some reason, he didn’t cite his recent book On the Wing: Insects, Pterosaurs, Birds, Bats and the Evolution of Animal Flight. By the way, David Alexander is not the same as R. McNeill Alexander, who published Principles of Animal Locomotion, which is also cited in the review, and who died earlier this year. The review cites several works by Mark Denny, although not my favorite: Air and Water. Alexander cites over a dozen works by Steven Vogel, whose Life in Moving Fluids appears on my ideal bookshelf. Finally, he writes that “James Gordon’s book Structures, or Why Things Don’t Fall Down (Gordon 1978) is one of the most entertaining and readable introductions to a technical topic ever written.” I read Gordon’s book many years ago and had almost forgotten it. Alexander is right, it is a gem.

In Figure 1.21, Russ Hobbie and I show a typical stress-strain curve. Alexander shows similar curves, and analyzes them in more detail. Like our book, he develops the concepts of Young’s modulus, shear modulus, strength, and Poisson’s ratio. Alexander introduces another concept: the strain energy density, which is the area under the stress-strain curve. Stress has units of N/m2, and strain is dimensionless, so the strain energy density has units of N/m2 = J/m3. Alexander writes "this key value measures how much work a material absorbs before breaking, and is sometimes referred to as ‘toughness’. Perhaps counterintuitively, some very hard, rigid materials are not very tough, whereas many floppy, easily extended materials are very tough.”

The section on fluid dynamics covers much of the same ground as analyzed in IPMB. It also discusses high Reynold’s number flow, including turbulence, flow separation, boundary layers, lift, and drag. These are fascinating topics, and are vital for understanding animal flight, but do not impact the low Reynold’s number flow that Russ and I focus on.

One topic that Russ and I give a brief mention is viscoelasticity. Alexander spends more time on this interesting subject.
“Most biological materials do not fit perfectly into the solid or fluid categories as engineers and physicists have usually defined them. Many biological structures that we would ordinarily consider solid actually have a time-dependent response to loading that gives them a partly fluid character. A proper Hookean material behaves the same way whether it is loaded for a second or a week: remove the load and it returns to its original shape. A viscoelastic solid, however, displays a property called creep : apply a load briefly and the material will spring back just as if it were Hookean. Apply the same load for a prolonged period, however, and the material will continue to deform gradually. When the load is removed, the material may have acquired a permanent deformation, and if so, the longer it is loaded, the greater the permanent deformation.”
Alexandar’s review is a great place to go for more about biomechanics after reading Chapter 1 of IPMB. I highly recommend it.

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