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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.
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 ...
The elastic properties can be well-characterized by the Young's modulus, Poisson's ratio, Bulk modulus, and Shear modulus or they may be described by the Lamé parameters. Young's modulus [ edit ]
By examining the formulas for area moment of inertia, we can see that the stiffness of this beam will vary approximately as the fourth power of the radius. Thus the second moment of area will vary approximately as the inverse of the density squared, and performance of the beam will depend on Young's modulus divided by density squared.
The Young's modulus of the test beams can be found using the bending IET formula for test beams with a rectangular cross section. The ratio Width/Length of the test plate must be cut according to the following formula: This ratio yields a so-called "Poisson plate".
where is the flexural modulus (in Pa), is the second moment of area (in m 4), is the transverse displacement of the beam at x, and () is the bending moment at x. The flexural rigidity (stiffness) of the beam is therefore related to both E {\displaystyle E} , a material property, and I {\displaystyle I} , the physical geometry of the beam.
For a material of Young's modulus, Y (same as modulus of elasticity λ), cross sectional area, A 0, initial length, l 0, which is stretched by a length, : = = where U e is the elastic potential energy.
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).