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Behavior of a structure under any loading condition is governed by its associated material/structural properties. Inhomogeneity and/or anisotropy in the material plays a crucial role in determining the response of such structures. In most of the cases, Functionally Graded Materials (FGMs), which are based on the idea of varied Young’s modulus of the material (inhomogeneity), ignore the contribution of Poisson’s ratio while Auxetic materials are solely based on the idea of variation of Poisson’s ratio. The consideration of variation of Poisson’s ratio show the capability to fine-tune the results for such analysis. In this work, Variational Asymptotic Method (VAM) has been adopted to analyze beam-type structure with constant Young’s modulus but varied Poisson’s ratio. The plots for strains have been drawn and compared with the results from FEA tool Abaqus. The plot behavior justifies the need to consider the variation of Poisson’s ratio in such analysis.

Power series method is used to analyze the distribution of stresses of the transversely isotropic cylinder under arbitrary axisymmetrical normal load. The stress function and normal load are expanded as the form of Fourier series. Unknown parameters in equations are determined using boundary conditions and final solutions of stress and displacement are obtained accordingly. The analysis of stresses obtained from different material parameters shows that the axial stress is significantly affected by Young's modulus and the circumference stress is sensitive to the variation of Poisson's ratio.

Barium chalcogenides are known for their high-technological importance and great scientific interest. Detailed studies of their elastic, mechanical, dynamical and thermodynamic properties were carried out using density functional theory and plane-wave pseudo potential method within the generalized gradient approximation. The optimized lattice constants were in good agreement when compared with experimental data. The independent elastic constants, calculated from a linear fit of the computed stress–strain function, were used to determine the Young’s modulus (E), bulk modulus (B), shear modulus (G), Poisson’s ratio ($\sigma$) and Zener’s anisotropy factor (A). Also, the Debye temperature and sound velocities for barium chalcogenides were estimated from the three independent elastic constants. The calculations of phonon dispersion showed that there are no negative frequencies throughout the Brillouin zone. Hence barium chalcogenides have dynamically stable NaCl-type crystal structure. Finally, their thermodynamic properties were calculated in the temperature range of 0–1000 K and their constant-volume specific heat capacities at room-temperature were reported.

Poisson’s ratios of two-dimensional (2D) all-inorganic perovskites Cs₂PbX₄ (X = Cl, Br, I) have been calculated by the first-principles calculations. The contribution of each geometric parameter (bond length $L$, bond angle $\mathrm{\Phi }$, rotation angle ${𝜃}_1$, and tilt angle ${𝜃}_2$) to Poisson’s ratio is obtained analytically. Through a comprehensive analysis of the geometric deformations of the perovskite under the uniaxial strain, we find that Poisson’s ratios of the perovskites are sensitive to the change of the bond length $L$ and the bond angle $\mathrm{\Phi }$. In addition, the value of the bond angle ${\mathrm{\Phi }}_0$ in the strain-free structure mainly determines the high in-plane anisotropy of Poisson’s ratios in Cs₂PbX₄.

Under the condition of small sample, the performance parameters’ interval quantization and instantaneous reliability calculation of solid rocket motor grain structure are researched. Two important mechanical properties of material: Relaxation modulus and Poisson’s ratio are obtained by experiments of grain material. Since the data of parameters obtained are a small sample, the method of gray theory is used to mine the experimental data. It realizes the uncertainty quantitative analysis of grain material performance parameters and obtains the quantitative interval of performance parameters. Considering that the evidence theory can directly attribute probabilistic mass to the set or interval, the instantaneous reliability of grain structure is analyzed based on the evidence theory. By establishing the relationship between failure surface and the frame of discernment, and using the belief function and plausibility function to obtain the upper and lower bound probability distribution of structural reliability and failure probability, the instantaneous reliability probability interval of structure is obtained.

The mechanical properties of cells are important in regulation of many aspects of cell functions. The cell may respond differently to a 2D plate and a 3D scaffold. In this study, the finite element analysis (FEA) was adopted to investigate mechanical deformation of chondrocyte on a 2D glass plate and chondrocyte seeded in a 3D scaffold. The elastic properties of the cell differ in these two different compression tests. This is because that the cell sensed different environment (2D plate and 3D construct) which can alter its structure and mechanical properties. It reveals how the apparent Poisson's ratio of a cell changes with the applied strain depends on its mechanical environment (e.g., the elastic moduli and Poisson's ratios of the scaffold and extracellular matrix) which regulates cell mechanics. In addition, the elastic modulus of the nucleus also plays a significant role in the determination of the Poisson's ratio of the cell for the cells seeded scaffold. It also reveals the intrinsic Poisson's ratio of the cell cannot be obtained by extrapolating the measured apparent Poisson's ratio to zero strain, particularly when scaffold's Poisson's ratio is quite different from the cell.

Poisson's ratio is an important factor for fracture of functionally graded materials (FGMs). It may have significant influence on fracture parameters (e.g. stress intensity factors and T-stress) for a crack in FGMs under mixed-mode loading conditions, while its effect on such parameters is negligible in homogeneous materials. For instance, when tension load is applied in the direction parallel to material gradation, the fracture parameters may show significant influence on the Poisson's ratio. This paper uses a new formulation, so-called non-equilibrium formulation, of the interaction integral method. It also presents a few numerical examples where Poisson's ratio is assumed either constant or linearly varying function, and Young's modulus is assumed to be exponential or hyperbolic-tangent function.

Peridynamics theory is a nonlocal meshless method that replaces differential equations with spatial integral equations, and has shown good applicability and reliability in the analysis of discontinuities. Further, with characteristics of clear physical meaning and simple and reliable numerical calculation, the bond-based peridynamics method has been widely applied in the field. However, this method describes the interaction between material points simply using a single elastic “spring”, and thus leads to a fixed Poisson’s ratio, relatively low computational efficiency and other inherent problems. As such, the goal of this review paper is to provide a summary of the various methods of bond-based peridynamics modeling, particularly those that have overcome the limitations of the Poisson’s ratio, considered the shear deformation and modeling of two-dimensional thin plates for bending and three-dimensional anisotropic composites, as well as explored coupling with finite element methods. This review will determine the advantages and disadvantages of such methods and serve as a starting point for researchers in the development of peridynamics theory.

Young's modulus and Poisson's ratio are the important parameters for representing the mechanical properties of soft tissue. Indentation test is an in vivo, non-invasive and convenient technique for measuring the tissue properties. In this chapter, two methods for the simultaneous estimation of Young's modulus and Poisson's ratio of soft tissues using indentation are presented. With the consideration of the finite deformation effect, the first method is based on the use of two sized indentors for conducting two different indentation tests, whereas the second one is only a single indentation test. Finite element (FE) analysis was used to demonstrate the feasibility of these two methods. The FE results were found to be comparable to the one shown in the previous literatures. It was revealed that finite deformation effect is of vital importance in the estimation of the Young's modulus and Poisson's ratio. Simultaneous estimation of these two parameters is necessary for achieving an accurate measurement of the Young's modulus.

The objective of this work was to propose a method for dynamic testing of Poisson's ratio of dimension lumber. Based on the first-order bending mode shape of cantilever slab, Sitka Spruce was selected as research object using instruments including four-channel dynamic resistance strain gauge and CRAS vibration and a set of collection-analysis system for dynamic signal. Free vibration of cantilever specimen of Sitka Spruce and mild steel can be stimulated by knocking, and the fundamental vibration should be reserved by filtering processing. Additionally, decaying curve of oscillatory waves for transverse and longitudinal strain of fundamental vibration should also be recorded and displayed. Obtained from the positive (negative) peak in oscillatory wave curve for transverse strain, Poisson's ratios along grain and across grain on radial section and that across grain on transverse section of Sitka Spruce specimens were measured. Then measured results were applied to analyse the accuracy of calculated modulus of elasticity obtained by plugging the first-order bending frequency measured by cantilever slab into equation of cantilever beam, and this method is proved to be robust and accurate. The method based on first-order bending mode shape of cantilever slab to measure dimension lumber Poisson's ratio is efficient and simple, with good repeatability and high accuracy. Besides, the same method was also applied to test Poisson’s ratio of mild steel to validate the correctness of the method on wood. It is observed that the positive (negative) peak in oscillatory wave curve for transverse strain is corresponding to that for longitudinal strain, meaning that the phase difference, between oscillatory wave curves for transverse strain and longitudinal strain, is 180°, or that transverse strain and longitudinal strain are reversed. The average value should be taken after calculating the ratios between peak-to-peak values read from the first channel and the second channel in oscillatory wave curve. The results show that the Poisson's ratio along grain of Sitka Spruce specimen is one order higher than that across grain, which indicates the anisotropy of wood. The test results validated that the elastic modulus of the lumber can be accurately derived by substituting the first-order fixed frequency, measured with the cantilever plate of Sitka Spruce specimen, into the cantilever theoretical equation. This research can provide reference to practical measurement and assessment of mechanical properties of wood and steel.