A simple model to describe the development of osteoporosis in long bones

Advanced theories exist in the literature to describe the extremely complex load-carrying mechanisms of real bone material. Necessarily, these models rely on constitutive equations involving numerous parameters that have to be determined by extensive (and expensive) experiments. The aim of the present paper, however, is to show that a very simple, one-dimensional model render first insights possible into the mechanical behavior of bone. Loss of mass and loss of connectivity are considered in a strength-of-materials type of theory. Based on constitutive equations with a lot of parameters and the well-known identification problems, a very simple, one-dimensional model is proposed to describe loss of mass and loss of connectivity in bone material. Based on thermodynamic considerations involving material forces, evolution equations for the associated internal variables are derived. The parameters of the model are adapted to experimental observations obtained from sheep with glucocorticoid treatment. The qualitative agreement between the results of the proposed model and other theoretical approaches as well as experimental results appears to be quite satisfactory. (C) 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim