First material-adapted force hypothesis for calculating equivalent stress in human femurs

Abstract

Strength hypotheses are assumptions, usually in the form of mathematical equations, which are applied in material science to convert multiaxial stress states in a material to a uniaxial stress state. Of particular interest regarding this conversion is the fact that the calculated uniaxial stress value in the material produces the same stress as the respective individual multiaxial stress. The "fictional" uniaxial stress determined in this way is also referred to as equivalent stress. Owing to the lack of experimental material data, many researchers and practitioners have in the past applied only the equivalent stress calculation based on the equations developed by von Mises under the assumption that the "material", bone, possesses isotropic properties. The present experimental work on selected human femora has been able for the first time, to quantify the anisotropy of these bones. At the same time a strength hypothesis has been formulated that can be used to convert multiaxial stress states for the material femoral bone to a uniaxial stress state (determination of equivalent stress).