A generalization of hooke's law in muscle elasticity

Experimental data concerning stress-strain relations of biological substances, including single muscle fibers, are reviewed in the literature. A reconsideration of the conclusions reached from these data is made. Thus, the experiments indicate that prima facie a linear theory of elasticity such as Hooke's law does not obtain because of the complicated form of the stress-strain curves. It is then shown that from a consideration oftrue stress at a point, where true stress is the force per unitactual area at the point, Hooke's law may be so generalized as to predict qualitatively and semi-quantitatively the complicated experimental curves. This complication arises from the long range “elasticity” of biological substances in general and muscle fibers in particular. Thus, substitutingtrue stress for stress, the stress-strain relation of muscle fibers remains linear. In the case of “small” strains, the true stress reduces to the usual stress concept in which the force is considered per unitinitial area at the point.