Scaling of Terrestrial Support: Differing Solutions to Mechanical Constraints of Size

Abstract

Terrestrial animals and plants span an enormous size range, and yet even distantly related groups are constructed of similar materials (e.g., bone, wood, muscle, and tendon). As with many physiological processes, evolutionary and ontogenetic changes in size impose constraints of scale on the mechanical design and function of skeletal support systems that are built of materials having similar properties. Adequate design requires that the capacity of skeletal elements (and muscles) for force transmission safely exceeds the levels required for biological support and movement. This is the case when the force transmitted per unit cross-sectional area of the material, defined as a mechanical stress (= F/,4, e.g., N/mm2), does not exceed the material's strength (the maximum stress that the material can withstand before faihrre). Clearly, larger structures can support larger forces more safely. The important design consideration, however, is whether changes in force requirements are matched by comparable changes in tissue cross-sectional area in order to keep maximal stresses and, thus, safety factors (defined as failure stress/peak functional stress) constant as size changes. Scale-invariant features (bone strength, timber strength, and peak muscle stress), therefore, require size-dependent changes in other features if the functional integrity of support systems is to be maintained over a broad size range (see also Li this volume). What are the features of terrestrial skeletal support systems that vary in a regular way with changes in size

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