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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 bulk modulus is an extension of Young's modulus to three dimensions. Flexural modulus ( E flex ) describes the object's tendency to flex when acted upon by a moment . Two other elastic moduli are Lamé's first parameter , λ, and P-wave modulus , M , as used in table of modulus comparisons given below references.
Once this material is attached to a rigid body at multiple locations, thermal stresses can be created in the geometrically constrained region. This stress is calculated by multiplying the change in temperature, material's thermal expansion coefficient and material's Young's modulus (see formula below).
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 ]
Bulk modulus: Ratio of pressure to volumetric compression (GPa) or ratio of the infinitesimal pressure increase to the resulting relative decrease of the volume; Coefficient of restitution: The ratio of the final to initial relative velocity between two objects after they collide. Range: 0–1, 1 for perfectly elastic collision.
The time-temperature superposition principle of linear viscoelasticity is based on the above observation. [5] Moduli measured using a dynamic viscoelastic modulus analyzer. The plots show the variation of elastic modulus E′(f, T) and the loss factor, tan δ(f, T), where δ is the phase angle as a function of frequency f and temperature T.
It measures the resonant frequencies in order to calculate the Young's modulus, shear modulus, Poisson's ratio and internal friction of predefined shapes like rectangular bars, cylindrical rods and disc shaped samples. The measurements can be performed at room temperature or at elevated temperatures (up to 1700 °C) under different atmospheres. [2]