Micromechanical finite element modeling

Van Rietbergen, B., Weinans, H, Huiskes, R., and Odgaard, A. (1995), A new method to determine trabecular bone elastic properties and loading using micromechanical finite element models, J. Biomech. 28(1) 69-81. 

Eshraghi, S., Das, S., 2012. Micromechanical finite-element modeling and experimental characterization of the compressive mechanical properties of polycaprolactone-hydroxyapatite composite scaffolds prepared by selective laser sintering for bone tissue engineering. Acta Biomaterialia 8 (8), 3138—3143. 

M.F. Horstemeyer et al Using a micromechanical finite element parametric study to motivate a phenomenological macroscale model for void/crack nucleation in aluminum with a hard second phase. Mech. Matls. 35, 675-687 (2003)... 

In particular it can be shown that the dynamic flocculation model of stress softening and hysteresis fulfils a plausibility criterion, important, e.g., for finite element (FE) apphcations. Accordingly, any deformation mode can be predicted based solely on uniaxial stress-strain measurements, which can be carried out relatively easily. From the simulations of stress-strain cycles at medium and large strain it can be concluded that the model of cluster breakdown and reaggregation for prestrained samples represents a fundamental micromechanical basis for the description of nonlinear viscoelasticity of filler-reinforced rubbers. Thereby, the mechanisms of energy storage and dissipation are traced back to the elastic response of tender but fragile filler clusters [24]. 

Micromechanics theories for closed cell foams are less well advanced for than those for open cell foams. The elastic moduli of the closed-cell Kelvin foam were obtained by Finite Element Analysis (FEA) by Kraynik and co-workers (a. 14), and the high strain compressive response predicted by Mills and Zhu (a. 15). The Young s moduli predicted by the Kraynik model, which assumes the cell faces remain flat, lie above the experimental data (Figure 7), while those predicted by the Mills and Zhu model, which assumes that inplane compressive stresses will buckle faces, lie beneath the data. The experimental data is closer to the Mills and Zhu model at low densities, but closer to the Kraynik theory at high foam densities. 

Khanna S.M., Flock A, and Ulfendahl M. 1989. Comparison of the tuning of outer hair cells and the basilar membrane in the isolated cochlea. Acta Otolaryngol. [Suppl] Stockholm 467 141-156. Kolston P.J. and Ashmore J.F. 1996. Finite element micromechanical modeling of the cochlea in three dimensions. /. Acoust. Soc. Am. 99 455-467. 

Ghosh, S. (2010) Micromechanical Analysis and Multi-scale Modeling Using the Voronoi Cell Finite Element Methods, CRC Press, Boca Raton, Florida. 

A numerical tool capable of predicting the mechanical behaviour of SWCNTs reinforced rubber. The formulation is based in a micromechanical, non-linear, multi-scale finite element approach and utilizes a Mooney-Rivlin material model for the rubber and takes into account the atomistic nanostructure of the nanotubes. The interfacial load transfer characteristics were parametrically approximated via the use of joint elements of variable stiffness. The SWCNTs improve significantly the composite strength and toughness especially for higher volume fractions. 

Figure 3.18e shows the effective force law (force versus displacement) between two parallel dimers with aspect ratio = 1.3 undergoing compression for the micromechanical model in which (1) lobe interactions are multiply counted or (2) the interaction potential is given by Equation 3.15. The two force laws are the same as long as overlaps between lobes have not merged, or < 0.021 for the configuration in Figure 3.18a. Beyond Sm, the two force laws differ. The force law based on the total area of overlap converges to linear behavior f 5 more quickly than the one that multiply counts lobe interactions, for example, it is not sensitive to the formation of the fourth lobe contact at 8/a = 84/a = 0.075. In future studies, these results can be compared to finite element analyses of linear elastic particles with complex shapes.

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