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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.
Using linear elastic indentation hardness, a relation between the ASTM D2240 hardness and the Young's modulus for elastomers has been derived by Gent [7].Gent's relation has the form = (+) (), where is the Young's modulus in MPa and is the ASTM D2240 type A hardness.
"Hardness" in the elastic range—a small temporary change in shape for a given force—is known as stiffness in the case of a given object, or a high elastic modulus in the case of a material. They exhibit plasticity—the ability to permanently change shape in response to the force, but remain in one piece.
In the case of indentation of an elastic half-space of Young's modulus using a rigid conical indenter, the depth of the contact region and contact radius are related by [17] ϵ = a tan ( θ ) {\displaystyle \epsilon =a\tan(\theta )}
This allows for the continuous evaluation of the hardness and Young's modulus of the material over the depth of the indentation, which is of great advantage with coatings and graded materials. The CSM method is also pivotal for the experimental determination of the local creep and strain-rate dependent mechanical properties of materials, as ...
[1]: 58 For example, low-carbon steel generally exhibits a very linear stress–strain relationship up to a well-defined yield point. The linear portion of the curve is the elastic region, and the slope of this region is the modulus of elasticity or Young's modulus. Plastic flow initiates at the upper yield point and continues at the lower ...
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 .
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: