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Design Safety
Published in Zohrab A. Samani, Hydraulic and Hydrologic Engineering, 2022
* Poisson’s ratio is the ratio of the proportional decrease in a lateral measurement to the proportional increase in length in a sample of material that is elastically stretched. In the absence of a measured Poisson’s ratio, use a conservative value of 0.25.
Mechanical Behavior of Materials
Published in Snehanshu Pal, Bankim Chandra Ray, Molecular Dynamics Simulation of Nanostructured Materials, 2020
Snehanshu Pal, Bankim Chandra Ray
Modulus of elasticity is higher for ceramic materials than for metals and polymers. On the other hand, metals have a high modulus of elasticity compared with polymers. The modulus of elasticity and shear modulus values, respectively, for a few metals are as follows: magnesium, 45 GPa and 17 GPa; aluminum, 69 GPa and 25 GPa; copper, 110 GPa and 46 GPa; nickel, 207 GPa and 76 GPa; steel, 210 GPa and 86 GPa; and tungsten, 410 GPa and 160 GPa, at room temperature [2]. Elastomers display higher elastic deformations than the onset of plastic deformation materials. The elastic materials that exhibit equal properties in all directions are known as isotropic elastic materials. Poisson’s ratio is defined as the ratio of lateral strain to longitudinal strain. The relationship between Young’s modulus (E), shear modulus (G), and Poisson’s ratio (μ) related to the isotropic materials is E=2G(1+μ) [3].
Steels
Published in M. Rashad Islam, Civil Engineering Materials, 2020
Poisson’s ratio can be defined as the ratio of lateral strain (εt) and longitudinal strain (εa). If tension force is applied axially on a body, its length increases and the lateral dimension decreases. If a compressive force is applied, the scenario is the opposite. Consequently, if lateral strain is positive, then longitudinal strain is negative, and vice-versa. Therefore, Poisson’s ratio is always negative, and its value is between 0 and 0.5. Mathematically, Poisson’s ratio can be expressed as (Eq. 9.7): μ=−εtεa=−ΔDDoΔLLo=−LateralStrainAxialStrain
Auxetic fibrous materials and structures in medical engineering – a review
Published in The Journal of The Textile Institute, 2023
Negative Poisson’s ratio (NPR) is exhibited by the auxetic structures or materials, by which they become thick, unlike ordinary materials, which tend to become thin when subjected to tensile load (Prawoto, 2012). Poisson’s ratio is defined as the negative ratio of the lateral or transverse strain to the longitudinal strain, The two strains are of the same physical quantity. Poisson’s Ratio is a pure number that means it has no dimension. The Poisson’s ratio is an elastic constant and is independent of the material scale. Auxeticity is due to correlated degrees of freedom in the internal elements. The elements whose Poisson’s ratio ranges from -∞ to 0 can be named auxetic. For isotropic materials, Poisson’s ratio (ν) lies between −1< ʋ< 1/2, for the anisotropic materials ʋ, can range from -∞ to +∞ (Ting & Chen, 2005).
Fracture of 28 buckled two-dimensional hexagonal sheets
Published in Mechanics of Advanced Materials and Structures, 2022
Minh-Quy Le, Huu-Tu Nguyen, Thanh-Lam Bui
For each 2D materials, a pristine squared sheet of 4032 atoms was initially generated by using its geometrical parameters at equilibrium at zero strain as listed in Table 1. Uniaxial tensile tests of pristine materials were a priori simulated to reveal their mechanical properties as shown in Tables 4 and 5. and ε denote the nominal axial stress (engineering stress) and nominal axial strain (engineering strain), respectively. Young’s modulus Y is determined by a linear fit of the stress-strain curve with 0≤ε ≤ 0.01. We denote here t as the sheet’s thickness. Yt and σt correspond to 2D Young’s modulus (or in plane-stiffness) and 2D stress (or in-plane stress), respectively. Poisson’s ratio is computed by taking the negative value of the ratio of the transverse strain to the axial strain.
In-plane impact dynamics of honeycomb structure containing curved reentrant sides with negative Poisson’s ratio effect
Published in Mechanics of Advanced Materials and Structures, 2022
Jianbang Shen, Jingran Ge, Junhua Xiao, Jun Liang
The Poisson’s ratio is used to define the relationship between the lateral deformation and the accompanying longitudinal deformation of the material. The NPR material will expand in the lateral direction when material occurs longitudinal tensile deformation, so the NPR material is also called Auxetics [7]. Since the successful manufacture of the first artificial NPR material from Lakes [8], more and more artificial NPR materials have emerged due to the rapid development of manufacturing and processing technology. According to the traditional honeycomb structure, the researchers have proposed the reentrant honeycomb structure [9]. Rotating rigid body structure based on rotation mechanism was proposed to explain the action mechanism of natural crystal NPR material. Then, based on this work, rotating quadrilateral structure [10] and rotating triangular structure [11] were proposed. The chiral structure, proposed by Lakes [12], was similar to human hands because it does not coincident with itself after mirroring, and the anti-chiral structure is exactly the opposite of it. Based on the deformation principle of the chiral structure, 3-, 4- and 6-connected chiral and back-hand honeycombs structures were obtained by changing the number of tangential beams around the rigid body [13], and the new chiral structure [14] was obtained by changing the shape of the tangential beam. NPR and compressive-twist deformation behavior appear in chiral-type cylindrical [15]. The NPR graphene-based carbon honeycomb has excellent performance in energy absorption [16, 17].