@ARTICLE{WoScSi08,
  author = {Wolfram, Uwe and Schwen, Lars Ole and Simon, Ulrich and Rumpf, Martin
	and Wilke, Hans-Joachim},
  title = {Statistical Osteoporosis Models Using Composite Finite Elements:
	A Parameter Study},
  journal = {Journal of Biomechanics},
  year = {2009},
  volume = {42},
  pages = {2205--2209},
  number = {13},
  month = {September},
  abstract = {Osteoporosis is a widely spread disease with severe consequences for
	patients and high costs for health care systems. The disease is characterised
	by a loss of bone mass which induces a loss of mechanical performance
	and structural integrity. It was found that transverse trabeculae
	are thinned and perforated while vertical trabeculae stay intact.
	For understanding these phenomena and the mechanisms leading to fractures
	of trabecular bone due to osteoporosis, numerous researchers employ
	micro finite element models. To avoid disadvantages in setting up
	classical finite element models, composite finite elements can be
	used. The aim of the study is to test the potential of composite
	finite elements. Furthermore, we are interested in whether changing
	trabecular diameters or losing trabeculae reduces macroscopic stiffness
	more. For that, a parameter study on numerical lattice samples with
	statistically simulated, simplified osteoporosis is performed. These
	samples are subjected to compression and shear loading. Results show
	that the worst drop of compressive stiffness is reached for transverse
	isotropic structures under $32\%$ isotropic trabecular degradation
	($89.7\%$ loss of the initial stiffness). Whereas the worst drop
	in shear stiffness is found for slightly transverse isotropic structure
	subjected to isotropic trabecular degradation of $32\%$ ($67.6\%$
	of the initial stiffness). The study indicates that losing trabeculae
	leads to a worse drop of macroscopic stiffness than thinning of trabeculae.
	The results further demonstrate that composite finite elements are
	an efficient simulation tool for micro-structured samples.},
  doi = {10.1016/j.jbiomech.2009.06.017},
  pdf = {http://numod.ins.uni-bonn.de/research/papers/public/WoScSi08.pdf},
}