Damaged elastic bone-column buckling theory within the context of adaptive elasticity.

Bone column-buckling is known as due to the loss of trabecular connectivity such that vertical weight-bearing trabeculae lose their cross attachments with each other. It has been considered as a predominant mechanism accounting for skeletal fragility disproportional to the degree of bone loss. Here, we focus our attention upon the improvement of our understanding of the relationships between bone degradation and fracture risk assessment (i.e., buckling load) which is both timely and at the core of important clinical problems such as osteoporosis and age-related bone fragility. With respect to well-known existing literature, there is a great need for a theoretical framework that provides new insights into the bending–buckling process when coupled to continuum damaged-bone adaptation. Within the limitations of our assumptions, it is clearly shown that damage occurs preferentially in regions where bone resorption activity dominates and the existence of a bone density gradient helps to maintain the stability of the bone-column deflection. For another, predicted buckling stress as a function of slenderness ratio is satisfactorily appreciated through experimental results. In our knowledge, this contribution is an original first attempt, at the scale of the single trabecula, which used adaptive elasticity in order to state an original but simplified adaptive-damage bone column buckling theory. [ABSTRACT FROM AUTHOR]