# poisson's ratio formula in terms of young's modulus

We use cookies to improve your website experience. The proof for this stems from the fact that E, G, and K are all positive and mutually dependent. Lett. Phys. Nat. *Correspondence: Alireza Mashaghi, Kavli Institute of Nanoscience, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, Netherlands e-mail: a.mashaghitabari@tudelft.nl, Front. Golden Delicious apples: mean value. Oxford: Butterworth-Heinemann. Interactions applied in the model. Similarly, for the gel and interdigitated phases, the initial temperatures were T = 1.08 and T = 1.16 and were switched to T = 1.2 and T = 1.3, respectively. We shall also learn the, Young’s Modulus Formula From Other Quantities. On the elastic modulus of metallic nanowires. 96, 101. doi:10.1529/biophysj.108.138677, Keywords: membrane mechanics, Young’s modulus, Poisson’s ratio, lipid bilayer, soft matter, Citation: Jadidi T, Seyyed-Allaei H, Tabar MRR and Mashaghi A (2014) Poisson’s ratio and Young’s modulus of lipid bilayers in different phases. where kc is the bending rigidity and σ is the surface tension. In materials science and solid mechanics, Poisson's ratio $${\displaystyle \nu }$$ (nu) is a measure of the Poisson effect, the deformation (expansion or contraction) of a material in directions perpendicular to the direction of loading. Lipid-Protein Interactions in Lipid Membranes. doi:10.1103/PhysRevA.33.3628, Hall, L., Coluci, V., Galvao, D., Kozlov, M., Zhang, M., Dantas, S., et al. The ratio of lateral strain and axial strain is defined as. Could we take Young's Modulus to be 2.2[GPa]? According to the Table 3 and Figure 4, fluid and interdigitated phases have the same measured Poisson’s ratio for both x and y-directions. Sci. Lenz, O. Phys. As such, efforts have been made to study the mechanical properties of bilayer patches with dimensions close to the mesh size of the actin cytoskeleton (Claesson et al., 2011). Rev. West, B. Determine Young’s modulus, when 2 N/m 2 stress is applied to produce a strain of 0.5. J. Mol. We have performed Monte Carlo simulations of the coarse grained lipid bilayer model to gain insight into the mechanical properties of planar lipid membranes. To investigate the power spectrum of the surfaces height fluctuations, we simulated a bilayer whose upper and lower leaflets consist of 64 × 64 lipid molecules. (6), one can obtain the according Young’s moduli. A generalized elastic theory for membranes with finite thicknesses was suggested by Brannigan and Brown (2006) and applied to the Lenz–Schmid model recently (West et al., 2009; Neder et al., 2010). Theoretical materials with a Poisson ratio of exactly 0.5 are truly incompressible, since the sum of all their strains leads to a zero volume change.Cork, on the other hand, has a Poisson ratio close to zero. Lett. Chem. 115, 4938–4950. Theoretical materials with a Poisson ratio of exactly 0.5 are truly incompressible, since the sum of all their strains leads to a zero volume change. Young’s modulus formula is given by, In the method, we present here the length between neighboring lipids is rescaled by a factor of (1 + η) in axial direction, let say y-direction, and the subsequent change of the simulation box size in perpendicular directions, in this case x- and z-direction, are monitored. Phys. The elastic behaviour of an isotropic, homogeneous, linear elastic medium can be completely described by two independent constants. The Young’s modulus is named after the British scientist Thomas Young. K = Bulk Modulus . However, this is not the case any more for the gel phase. In this method, the Poisson’s ratio is calculated by utilizing a rescaling of inter-particle distances in one lateral direction under periodic boundary conditions. One more thing, still I don't know the value of Poisson's ratio, could you please help me, I am trying to practice COMSOL tutorial Application ID: 417 ( Acoustic-Structure Interaction). The Poisson ratio of crystalline surfaces. Biophys. Bending modulus of lipid bilayers in a liquid-crystalline phase including an anomalous swelling regime estimated by neutron spin echo experiments. doi:10.1016/S0006-3495(02)75479-9, Brannigan, G., and Brown, F. L. H. (2006). Utilizing the periodic boundary conditions, we introduce a method to compute the Poisson’s ratio for the surface (Abedpour et al., 2010). Beads belonging to one molecule are connected via finitely extensible non-linear elastic (FENE) springs (Grest and Kremer, 1986) with a bond stretching potential Figure 1: Figure 1. The Young’s modulus and Poisson’s ratio are interrelated by formula that incorporate the bending rigidity, but neither Young’s modulus nor Poisson’s ratio have been determined separately so far. This makes cork function well as a bottle stopper, since an axially-loaded cork will not swell laterally to resist bottle insertion. Obviously, the observed anisotropicity in the gel phase dose not allow to use the above theorem for the bilayer in this phase. Young’s modulus is also known as modulus of elasticity and is defined as: The mechanical property of a material to withstand the compression or the elongation with respect to its length. Simulations were performed under constant temperature and pressure condition (NPT ensemble) for lipid bilayers with different sizes. Elastic properties play an important role in a number of membrane processes, as for example, membrane fusion (Chernomordik and Kozlov, 2008) and modulations of membrane channel activities (Schmidt and MacKinnon, 2008; Sansom and Biggin, 2010; Mashaghi et al., 2013b). 88, 1104–1119. This means that if you have any two elastic constants, you can calculate any other. • Hope you understood modulus of elasticity and Young’s modulus in this article. Biochim. Young’s modulus is also used to determine how much a material will deform under a certain applied load. Molecular dynamics simulation of NMR relaxation rates and slow dynamics in lipid bilayers. Copyright: © 2014 Jadidi, Seyyed-Allaei, Tabar and Mashaghi. Common sense (and the 2nd Law of Thermodynamics) indicates that a material under uniaxial tension must elongate in length. The value of Poisson's ratio is the negative of the ratio of transverse strain to axial strain. Biophys. Sansom, D. M. S. P., and Biggin, P. C. (2010). 4) decreases for more than 43% and Lame's coefficient µ for 42.3%. Ph.D. thesis, University of Bielefeld, Bielefeld. (5). J. Another way to prevent getting this page in the future is to use Privacy Pass. Lipid’s head beads and tail bead are shown in red and green, respectively. Tables for Calculating the Compressive Surface Stresses and Deflections in the Contact of Two Solid Elastic Bodies whose Principle Planes of Curvature do not Coincide, Poisson's ratio and Young's Modulus for Apple Flesh, Dynamic Elastic Properties of Some Fruits during Growth and Development. (5). A simple computer model for liquid lipid bilayers. B 116, 6455–6460. Mean value of Poisson's ratio (ν) is 0.173 during the first 139 days cold storage, afterwards this mean value increases to reach 0.221 after 186 days. For small values of these changes, $${\displaystyle \nu }$$ is the amount of transversal elongation divided by the amount of axial compression. Conversely, when the bilayer was extended in the perpendicular direction to the tilt plane, lipids reorganize themselves in such a way that the bilayer laterally shrank. For a membrane of lateral size L × L, Eq. The Young’s Modulus of such a material is given by the ratio of stress and strain, corresponding to the stress of the material. Europhys. Most materials have Poisson's ratio values ranging between 0.0 and 0.5. Snapshots of the simulated lipid membrane in the (A) gel, (B) fluid, and (C) interdigitated phase. The measurements show that, a bilayer in the gel phase behaves as an anisotropic material, which has two distinguishably different values for the two different directions in the plane of the bilayer. The approach may be applied to other membranes such as graphene and tethered membranes in order to predict the temperature dependence of its Poisson’s ratio and Young’s modulus. There are other numbers that give us a measure of elastic properties of a material, like Bulk modulus and shear modulus, but the value of Young’s Modulus is most commonly used. Young's modulus Poisson's ratio n' = - de r / de a. Fluctuation spectra for the fluid, gel, and interdigitated phases and fits to the Eq. Solution: Given:Stress, σ = 2 N/m 2 Strain, ε = 0.5 Young’s modulus formula is given by, E = σ / … The spectral density for the interdigitated phase was calculated according to the same method. E = σ / ϵ = 2 / 0.5 =4 N/m2. Determine Young’s modulus of a material whose elastic stress and strain are 4 N/m2 and 0.15 respectively? Evolution of Young's modulus (E), Poisson's ratio (ν) and Lame's coefficients (λ and μ) during a 186 days cold storage (2°C, 96% hr). Figure 4. (2008). Microsyst.

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