A Study to Derive Equivalent Mechanical Properties of Porous Materials with Orthotropic Elasticity

The need for diverse materials has emerged as industry becomes more developed, and there is a need for materials with pores in various industries, including the energy storage field. However, there is difficulty in product design and development using the finite element method because the mechanical properties of a porous material are different from those of a base material due to the pores. Therefore, in this study, a Python program that can estimate the equivalent property of a material with pores was developed and its matching was verified through comparison with the measurement results. For high-efficiency calculation, the pores were assumed to be circular or elliptical, and they were also assumed to be equally distributed in each direction. The material with pores was assumed to be an orthotropic material, and its equivalent mechanical properties were calculated using the equivalent strain and equivalent stress by using the appropriate material property matrix. The material properties of a specimen with the simulated pores were measured using UTM, and the results were compared with the simulation results to confirm that the degree of matching achieved 6.4%. It is expected that this study will contribute to the design and development of a product in the industrial field.

Hypersingular boundary integral equations for plane orthotropic elasticity in terms of first-order stress functions

This paper is intended to present an implementation of the hypersingular boundary integral equations in terms of first-order stress functions for stress computations in plane orthotropic elasticity. In general, the traditional computational technique of the boundary element method used for computing the stress distribution on the boundary and close to it is not as accurate as it should be. In contrast, the accuracy of stress computations on the boundary is greatly increased by applying the hypersingular integral equations. Contrary to the method in which the solution is based on an approximation of displacement field, here the first-order stress functions and the rigid body rotation are the fundamental variables. An advantage of this approach is that the stress components can be obtained directly from the stress functions, there is, therefore, no need for Hooke's law, which should be used when they are computed from displacements. In addition, the computational work can be reduced when the stress distribution is computed at an arbitrary point on the boundary. The numerical examples presented prove the efficiency of this technique.

The Effect of the Anisotropy of Single Crystal Silicon on the Frequency Split of Vibrating Ring Gyroscopes

This paper analyzes the effect of the anisotropy of single crystal silicon on the frequency split of the vibrating ring gyroscope, operated in the n = 2 wineglass mode. Firstly, the elastic properties including elastic matrices and orthotropic elasticity values of (100) and (111) silicon wafers were calculated using the direction cosines of transformed coordinate systems. The (111) wafer was found to be in-plane isotropic. Then, the frequency splits of the n = 2 mode ring gyroscopes of two wafers were simulated using the calculated elastic properties. The simulation results show that the frequency split of the (100) ring gyroscope is far larger than that of the (111) ring gyroscope. Finally, experimental verifications were carried out on the micro-gyroscopes fabricated using deep dry silicon on glass technology. The experimental results are sufficiently in agreement with those of the simulation. Although the single crystal silicon is anisotropic, all the results show that compared with the (100) ring gyroscope, the frequency split of the ring gyroscope fabricated using the (111) wafer is less affected by the crystal direction, which demonstrates that the (111) wafer is more suitable for use in silicon ring gyroscopes as it is possible to get a lower frequency split.

Dependence of Poisson’s ratio and Young’s modulus on microfibril angle (MFA) in wood

Microfibril angle (MFA) is a major structural variable that describes the fine structure of the cell wall in wood. In this study, the relationships between the MFA of the S2 layer and the Poisson’s ratios and Young’s moduli (modulus of elasticity, MOE) of five wood species (agathis, larch, Japanese cedar, Japanese cypress and ginkgo) were determined by analyzing both their normal and compression woods. It was found that both the longitudinal MOE (MOEL) and MOE of the cell-wall substance (MOEW) decreased with increasing MFA, while the peaks values of Poisson’s ratio (νLT) were obtained at MFAs of ≈25°. In particular, at MFAs lower than 25°, theνLTincreased with increasing MFA, and the opposite relationship was observed at MFA values exceeding 25°. This trend is in good agreement with the estimates obtained based on the theory of orthotropic elasticity with the underlying assumption that the orthotropic elasticity of materials is MFA-dependent. Hence, the MFA parameter incorporated into the orthotropic elasticity theory is useful for determination of the Poisson’s ratio.