Numerical Homogenization in Multi-scale Models of Musculoskeletal Mineralized Tissues

A. Gerisch[1], S. Tiburtius[1], Q. Grimal[2], and K. Raum[3]
[1]Technische Universität Darmstadt, Darmstadt, Germany
[2]Laboratoire d’Imagerie Paramétrique, UPMC, Paris, France
[3]Julius Wolff Institut & Berlin-Brandenburg School for Regenerative Therapies, Charité-Universitätsmedizin Berlin, Berlin, Germany
Published in 2011

Musculoskeletal mineralized tissues (MMTs), e.g. bone, are hierarchical composite materials. Their effective elastic properties at different scales are of interest for computational studies of the MMT’s response to mechanical loading but also to realistically simulate implant osseointegration.

We combine multi-scale and multi-modal experimental techniques with mathematical modelling of MMTs and obtain a hierarchy of models from the sub-micrometer to the millimeter scale. Analytical and numerical homogenization techniques are employed to connect elastic properties at increasingly coarser scales. From this hierarchy of models, a set of experimentally validated anisotropic elastic stiffness tensors at different length scales is derived. These tensors provide the basis for macro-scale Finite Element studies and hence contribute to address further research questions.