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Young's modulus ( E) describes tensile and compressive elasticity, or the tendency of an object to deform along an axis when opposing forces are applied along that axis; it is defined as the ratio of tensile stress to tensile strain. It is often referred to simply as the elastic modulus.
The stress–strain curve for a ductile material can be approximated using the Ramberg–Osgood equation. This equation is straightforward to implement, and only requires the material's yield strength, ultimate strength, elastic modulus, and percent elongation. Toughness Toughness as defined by the area under the stress–strain curve
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 elasticity tensor is a fourth-rank tensor describing the stress-strain relation in a linear elastic material. [1] [2] Other names are elastic modulus tensor and stiffness tensor. Common symbols include and . The defining equation can be written as. where and are the components of the Cauchy stress tensor and infinitesimal strain tensor, and ...
The three-point bending flexural test provides values for the modulus of elasticity in bending , flexural stress , flexural strain and the flexural stress–strain response of the material. This test is performed on a universal testing machine (tensile testing machine or tensile tester) with a three-point or four-point bend fixture.
Its tensile stress σ is linearly proportional to its fractional extension or strain ε by the modulus of elasticity E: σ = E ε . {\displaystyle \sigma =E\varepsilon .} The modulus of elasticity may often be considered constant.
Stress-strain relations. For a homogeneous isotropic linear elastic material, the stress is related to the strain by =, where is the Young's modulus. Hence the stress in an Euler–Bernoulli beam is given by
The requirement of the symmetry of the stress and strain tensors lead to equality of many of the elastic constants, reducing the number of different elements to 21 = = =. An elastostatic boundary value problem for an isotropic-homogeneous media is a system of 15 independent equations and equal number of unknowns (3 equilibrium equations, 6 ...