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Young's modulus is defined as the ratio of the stress (force per unit area) applied to the object and the resulting axial strain (displacement or deformation) in the linear elastic region of the material. Although Young's modulus is named after the 19th-century British scientist Thomas Young, the concept was developed in 1727 by Leonhard Euler.
Elastic properties describe the reversible deformation (elastic response) of a material to an applied stress.They are a subset of the material properties that provide a quantitative description of the characteristics of a material, like its strength.
Young's modulus (E) - apply small, incremental changes in the lattice parameter along a specific axis and compute the corresponding stress response using DFT. Young’s modulus is then calculated as E=σ/ϵ, where σ is the stress and ϵ is the strain. [4] Initial structure: Start with a relaxed structure of the material.
E 1 and E 2 are the Young's moduli in the 1- and 2-direction and G 12 is the in-plane shear modulus. v 12 is the major Poisson's ratio and v 21 is the minor Poisson's ratio. The flexibility matrix [S] is symmetric. The minor Poisson's ratio can hence be found if E 1, E 2 and v 12 are known.
The Poisson's ratio of a stable, isotropic, linear elastic material must be between −1.0 and +0.5 because of the requirement for Young's modulus, the shear modulus and bulk modulus to have positive values. [3] Most materials have Poisson's ratio values ranging between 0.0 and 0.5.
Young's Mathematical Elements of Natural Philosophy. Young described the characterization of elasticity that came to be known as Young's modulus, denoted as E, in 1807, and further described it in his Course of Lectures on Natural Philosophy and the Mechanical Arts. [39]
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Volume, modulus of elasticity, distribution of forces, and yield strength affect the impact strength of a material. In order for a material or object to have a high impact strength, the stresses must be distributed evenly throughout the object. It also must have a large volume with a low modulus of elasticity and a high material yield strength. [7]