RESUMO
A very low-frequency mode supported within an auxetic structure is presented. We propose a constrained periodic framework with corner-to-corner and edge-to-edge sharing of tetrahedra and develop a kinematic model incorporating two types of linear springs to calculate the momentum term under infinitesimal transformations. The modal analysis shows that the microstructure with its two degrees of freedom has both low- and high-frequency modes under auxetic transformations. The low-frequency mode approaches zero frequency when the corresponding spring constant tends to zero. With regard to coupled eigenmodes, the stress-strain relationship of the uniaxial forced vibration covers a wide range. When excited, a very slow motion is clearly observed along with a structural expansion for almost zero values of the linear elastic modulus.
RESUMO
The effect of Ti, V and Al ions on the relative growth rate of L929 cells and MC3T3-E1 cells was investigated by a cell culture method with metallic powders. These powders were sterilized under a U.V. lamp for 6 h, suspended in the medium and extracted for 48 h, 72 h and 96 h in the incubator. After filtering with a 0.2 microns filter, 3.0 x 10(4) L929 cells and 5 x 10(4) MC3T3-E1 cells were seeded in these filtrates of the medium with and without (control) the presence of the metallic powder. The number of cells was counted using a coulter counter from 1 to 7 days. The number of L929 cells after 4 days of incubation was almost similar for Ti and the control, whereas in the case of A1 and V extraction the number of cells was too low as compared to that of the control. The relative growth rate of L929 cells for Ti, A1 and V after 4 days of incubation was about 1, 0.2 and 0.02, respectively. A similar trend was also observed for MC3T3-E1 cells. The effect of the relative growth rate of L929 cells at different extraction times of 48 h, 72 h and 96 h was examined. It was found that the relative growth rate of L929 cells for Ti, A1 and V extraction was almost the same at all three extraction times. A number of 2.0-5.0 x 10(4) cells was seeded in the medium of A1 extraction. The effect of this initial number of cells on the relative growth rate of L929 cells was investigated. The relative growth rate of L929 cells decreased as the initial number of L929 cells increased. Moreover, dilutions from 1 to 10 times in the case of A1 and from 1 to 4000 times in the case of V were made. The relative growth rate became equal to 1 at 5 times dilution for A1 and at 4000 times dilution for V, for both L929 and MC3T3-E1 cells. From the measures of the concentration of the released A1 and V ions on the relative growth rate of L929 cells, it could be seen that there was a marked decrease in the concentrations of A1 and V ions from 0.3 ppm to 0.1 ppm.
