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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 .
The strength of materials is determined using various methods of calculating the stresses and strains in structural members, such as beams, columns, and shafts. The methods employed to predict the response of a structure under loading and its susceptibility to various failure modes takes into account the properties of the materials such as its yield strength, ultimate strength, Young's modulus ...
Young's modulus: E: Ratio of stress to strain pascal (Pa = N/m 2) L −1 M T −2: scalar; assumes isotropic linear material spring constant: k: k is the torsional constant (measured in N·m/radian), which characterizes the stiffness of the torsional spring or the resistance to angular displacement. N/m M T −2: scalar
The slope of the initial, linear portion of this curve gives Young's modulus. Mathematically, Young's modulus E is calculated using the formula E=σ/ϵ, where σ is the stress and ϵ is the strain. Shear modulus (G) Initial structure: Start with a relaxed structure of the material. All atoms should be in a state of minimum energy with no ...
Isotropic elastic properties can be found by IET using the above described empirical formulas for the Young's modulus E, the shear modulus G and Poisson's ratio v. For isotropic materials the relation between strains and stresses in any point of flat sheets is given by the flexibility matrix [S] in the following expression:
Young's modulus and shear modulus are only for solids, whereas the bulk modulus is for solids, liquids, and gases. The elasticity of materials is described by a stress–strain curve , which shows the relation between stress (the average restorative internal force per unit area) and strain (the relative deformation). [ 2 ]
The actual elastic modulus lies between the curves. In materials science , a general rule of mixtures is a weighted mean used to predict various properties of a composite material . [ 1 ] [ 2 ] [ 3 ] It provides a theoretical upper- and lower-bound on properties such as the elastic modulus , ultimate tensile strength , thermal conductivity ...