The foot as a shock absorber

A mathematical analysis of the deformation of the foot is developed to determine the role that stretch of ligaments and tendons plays in absorbing shock following impact. Our analysis is based on an anatomical biomechanical model that includes each of the bones of the foot. We calculate the time course of the deflection of the joints and the elongation of the ligaments and tendons and determine the ground reaction force acting on the heel. Quasi-linear viscoelastic theory is used for soft tissue constitutive relationships. With biomechanical data selected from the literature, we obtain a vertical force impact peak of 8000 N, occurring at 16 ms following heel strike. This is of higher magnitude and shorter duration than is found experimentally, as is to be expected, since we did not include the heel pad in our model and we assumed that the impact surface was ideally rigid.