By using Neuber's rule, tooth root stresses predicted by means of two-dimensional elastic finite element analysis are translated into estimates of elastic-plastic stress and strain behaviour.
Theoretical model based on differential scheme predicts a good estimate of elastic modulus for all the type of GMB/HDPE foams.
In most cases, the estimate of elastic modulus is more sensitive to these uncertainties than the estimate of diffusion coefficient, and the effects of uncertainty of the partial molar volume are of utmost importance.
However, in the case of relatively small concentrations of hydrogen, uncertainty of the specimen's thickness is most important for the estimate of elastic modulus acquired from one-port flux TF, while the estimates of both parameters acquired from the concentration TF are immune to the uncertainties discussed here.
The GMC homogenizer is found to provide better estimates of effective elastic properties than the finite element based homogenizer for composites with particle volume fractions less than 0.80.
The presented analytical expression is believed to be general and provide accurate estimates of the elastic properties of a wide range of foam materials, provided that their bulk material properties and micro structure can be established.
The results of the presented theory are compared with experimental data on composite materials which show that good estimates of the elastic moduli can be achieved by using statistical multi step homogenization technique.
A comparison of sensitivity of the estimates of bulk elastic modulus of the M H system and diffusion coefficient of hydrogen, acquired from three alternative transfer functions (TFs) of transport of hydrogen through a thin membrane specimen of metal, was performed with respect to the uncertainty of equilibrium concentration of hydrogen, its partial molar volume and thickness of the specimen.
Results demonstrate that simple analytic models provide good estimates of the elastic properties of the porous Ti and that the moduli can be significantly reduced to decrease the mismatch between solid Ti and bone.
In our experiments, the direction of applied forces and the selected component of the resulting displacements were conveniently paired in order to reproduce the elements of the Green's tensor that provided direct estimates of the elastic moduli (Fig. 1, lower row).
