Studies on bone remodelling theory based on microcracks
|Bearbeitung:||Prof. Dr.-Ing. Udo Nackenhorst, Dipl.-Ing.(FH) Dieter Kardas|
|Förderung durch:||This work is supported by the Research training group 615 of the DFG (German Research Foundation)|
Normally after the age of 16 years, the cortical bone section shows a structured costitution. Here two different bone types apprear: Lamellar and osteonal bone. Due to the composition of collagen fibers and attached mineral cristals, bone has an anisotropic behavior. Furthermore lacunas (inclusions where osteocytes are housed) cause an highly inhomogenious behavior.
Figure 1: Microcrack growing inside lamellar bone matrix. The amount of damage is displayed as radius of the ellipsoids.
The studies in this work are based on our assumption that shear stresses near the lacunas initiate microcracks. To verify this assumption a 3D lamellar bone part with imperfections, representing lacunas, has been simulated, as a first approximation. First step of this simulation is the computation of the composite bone material. Here the Mori Tanaka homogenitzation method maps the properties of the nanometer structure to the micrometer structure, where the second simulation step takes place. At the micro level the fiber reinforced like structure of collagen and mineral cristals is built up in cross ply layers. Lacunas are present direct at the border faces between these layers. These imperfections are idealized as low stiffness elememts. In simulations, in-plane shear stresses at the lacunas are dominant (figure 2). To compute microcracks, a constitutive material model with nonlinear softening was implemented in the FE code. The criterion used, which decides whether a crack arises or not, is based on the formulations of Brewer-Lagace. This delamination model takes into accout in-plane shear stresses and the stress component normal to the plane (figure 3). With this formulation, it is possible to compute microcracks in cortical bone (figure 1). Therefore the goal of this work will be a constitutive model development based on micromechnical pheonomenas.
Figure 2: In-plane shear stress distribution during crack propagation
Figure 3: Brewer-Lagace stress norm distribution during crack propagation.