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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 first stage is the linear elastic region. The stress is proportional to the strain, that is, obeys the general Hooke's law, and the slope is Young's modulus. In this region, the material undergoes only elastic deformation. The end of the stage is the initiation point of plastic deformation.
The compressive strength of the material corresponds to the stress at the red point shown on the curve. In a compression test, there is a linear region where the material follows Hooke's law. Hence, for this region, =, where, this time, E refers to the Young's modulus for compression. In this region, the material deforms elastically and returns ...
The natural frequency of this flexural vibration mode is characteristic for the dynamic Young's modulus. To minimize the damping of the test-piece, it has to be supported at the nodes where the vibration amplitude is zero. The test-piece is mechanically excited at one of the anti-nodes to cause maximum vibration. Test-piece vibrating in the ...
Tensile testing, also known as tension testing, [1] is a fundamental materials science and engineering test in which a sample is subjected to a controlled tension until failure. Properties that are directly measured via a tensile test are ultimate tensile strength , breaking strength , maximum elongation and reduction in area. [ 2 ]
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 shear modulus is one of several quantities for measuring the stiffness of materials. All of them arise in the generalized Hooke's law: . Young's modulus E describes the material's strain response to uniaxial stress in the direction of this stress (like pulling on the ends of a wire or putting a weight on top of a column, with the wire getting longer and the column losing height),