The aim of this study was to evaluate the influence of microstructural parameters, such as porosity and osteon dimensions, on strength. Therefore, the predictive value of bone mineral density (BMD) ...measured by quantitative computed tomography (QCT) for intracortical porosity and other microstructural parameters, as well as for strength of cortical bone biopsies, was investigated. Femoral cortical bone specimens from the middiaphysis of 23 patients were harvested during total hip replacement while drilling a hole (dia. 4.5 mm) for the relief of the intramedullary pressure. In vitro structural parameters assessed in histological sections as well as BMD determined by quantitative computed tomography were correlated with yield stress, and elastic modulus assessed by a compression test of the same specimens. Significant correlations were found between BMD and all mechanical parameters (elastic modulus: r = 0.69, p < 0.005; yield stress: r = 0.64, p < 0.005). Significant correlations between most structural parameters assessed by histology and yield stress were discovered. Structural parameters related to pore dimensions revealed higher correlation coefficients with yield stress (r = −0.69 for average pore diameter and r = −0.62 for fraction of porous structures, p < 0.005) than parameters related to osteons (r = 0.60 for osteon density and average osteonal area, p < 0.005), whereas elastic modulus was predicted equally well by both types of parameters. Significant correlations were found between BMD and parameters related to porous structures (r = 0.85 for porosity, 0.80 for average pore area, and r = 0.79 for average pore diameter in polynomial regression, p < 0.005). Histologically assessed porosity correlated significantly with parameters describing porous structures and haversian canal dimensions. Our results indicate a relevance of osteon density and fraction of osteonal structures for the mechanical parameters of cortical bone. We consider the measurement of BMD by quantitative computed tomography to be helpful for the estimation of bone strength as well as for the prediction of intracortical porosity and parameters related to porous structures of cortical bone.
Even in the range of small elastic deformations the behavior of foams is not well described by only two elastic constants. Usually the manufacturers give values of the material parameters depending ...on the loading conditions. This problem is investigated on a microscopic scale by a simple beam model and on the macroscopic scale by an extended continuum model. It has been found that this approach shows the size effect
J. Mater. Sci. 18 (1983) 2572 that cannot be described within the framework of the standard continuum mechanical setting. The existence of the size effect within this model can be explained by independent rotations which do not scale with the displacement field.
While macroscopic material parameters are generally unknown for foams the macroscopic properties are derived from the microscale where the parameters are assumed to be known. After evaluation of the microscopic constitutive equations, which are also considered to be known, the quantities are mappped back to the macroscale by a homogenization procedure. This approach is known from literature as FE
2 model, see e.g. V. Kouznetsova, Computational homogenization for the multi-scale analysis of multi-phase materials, PhD-thesis, Technical University of Eindhoven, 2002, Int. J. Numer. Meth. Eng., 54 (2002) 1235 or Arch. Appl. Mech., 72 (2002) 300. It is shown that the Cosserat continuum and the FE
2 model are able to describe the same effects qualitatively.
Materials with inherent microstructures like granular media, foams or spongy bones often show a complex constitutive behaviour on the macroscale while the microscopic constitutive equations may be ...formulated in a simple fashion. Applying homogenization procedures allows to transfer the information from the microlevel to the macrolevel.In the present contribution the porous structure of hard biological tissues, i.e. of spongy bones, is investigated. On the macroscale the approach is embedded into an extended continuum mechanical setting in order to capture size effects. The constitutive equations are formulated on the microscopic level taking into account growth and reorientation of the microstructural elements. By application of a strain-driven numerical homogenization procedure the macroscopic stress response is obtained.
The mechanical behavior of open-cell foams may be modeled either on a microscopic or a macroscopic scale. In the first case, the behavior of the individual cell walls is described by beam models, ...while in the second case a continuum mechanical approach is applied. Both approaches have different advantages: On the one hand, the microscopic approach allows for a simple formulation of the constitutive equations but requires detailed knowledge of the heterogeneous microstructure, e.g. geometrical data of the beams and of the topology, and becomes numerically expensive for large structures. On the other hand, the macroscopic approach leads to efficient computations but requires more complicated constitutive equations, if e.g. anisotropy is taken into account.In the present contribution the advantages of the microscopic and macroscopic descriptions are combined by a numerical so-called second order homogenization scheme. Therefore, a small but representative element of the microstructure consisting of a few beam elements is chosen and attached to the quadrature points of the macroscopic finite element model. The macroscopic model is formulated in the framework of a Cosserat continuum, which allows to take care of size effects. The macroscopic strain and curvature tensors are projected onto the microstructure leading to a deformation mode of the beam ensemble. The resulting forces and moments in the beams are homogenized by an appropriate averaging procedure defining the corresponding stresses and couple stresses on the macroscale. In this approach, anisotropy is included in a natural way choosing an anisotropic distribution of the beams in the testing volume element (TVE). In addition, damage is described on the microscopic level of the individual beams.
In a prospective randomized clinical trial, ADCON-T/N was investigated with regard to its effectiveness in fresh traumatic injuries of the flexor tendons in Zone II of the hand. Thirty patients ...participated in the trial. Following a standardized technique of tendon repair, the total active motion (TAM) and total extension lag (TEL) were determined after 12 weeks and evaluated according to the Buck-Gramcko score. Excellent results were achieved in 15 out of 16 patients in the ADCON-T/N group and 12 out of 14 in the control group. However, no statistically significant difference was found between the mean TAM and TEL in the two groups.
The deformation of a beam lattice is investigated as a two‐dimensional model of a foam. Forces, moments, displacements and rotations are averaged leading to stress, couple stress, strain and ...curvature on the macroscale. Therefore, the effective medium is assumed to be micropolar.
