Simulation of material property evolution of cortical bone in bending fatigue and its implications on cancellous bone

Cotton, J.R., Zioupos, P. and Taylor, M. (2001) Simulation of material property evolution of cortical bone in bending fatigue and its implications on cancellous bone. International Society of Biomechanics XVIIIth Congress, Zurich, Switzerland. 07 - 12 Jul 2001. pp. 215-216 .

Abstract

Taylor (1999) presented a model describing fatigue life, modulus degradation, and permanent strain growth of cortical bone under uniaxial fatigue. In our ongoing work, we are seeking to model cancellous bone with individual trabeculae behaving as cortical bone. When a cancellous lattice is loaded uniaxially, bending occurs within and is the primary mode of deformation, as well as the cause of high stress concentrations. In this work, we simulate bone in pure bending using the Taylor material model. This provides a simple scenario where material property evolution results in a passive redistribution of stresses.
Methods: Taylor's model was combined with equations of equilibrium and an assumed linear strain profile to form the theoretical basis of this model. We also assumed that the strain at any height was the sum of elastic strain and damage-dependant permanent strain. Elastic strain was assumed linear elastic with a damage-dependant modulus. Equations were nondimensionalized and coded for computational solution. We deactivated individual aspects of the model (life, modulus degradation, plastic strain growth) for some studies so each effect could be studied independently. We examined the life per applied stress (S-N curve), as well as the distribution of stress, strains, damage, and modulus through the section during the life.
Results and Discussion: During the simulation, high stresses at the tensile, and to a lesser extent the compressive, surface resulted in high damage there. This caused localized modulus degradation and plasticity, along with stress realignment. Stress profiles are shown in the figure below from a case with initial peak strain of 0.008. (Height of 1 in the compressive side, -1 is in tension.)
The presence of modulus degradation increased the number of cycles to failure. Adding plasticity further increased the life. This may seem counter-intuitive if one thinks of these processes as undesirable, but the ability to equalize stress distribution results in a beam more resistant to failure.

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