Learning topic
Elastic Properties of Materials
Young's modulus E, shear modulus G, Poisson's ratio ν, and their physical meaning in linear-elastic deformation calculations.
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Elastic properties describe a material's resistance to reversible deformation. For a linearly elastic isotropic material, the principal constants include Young's modulus $E$, shear modulus $G$, and Poisson's ratio $\nu$.
Within the linear-elastic range, normal stress is proportional to axial strain:
$$\sigma=E\varepsilon.$$
- $\sigma$ — normal stress, Pa or MPa;
- $E$ — Young's modulus, Pa or MPa;
- $\varepsilon$ — axial strain, dimensionless.
The law applies to the linear portion of the stress–strain curve while $\sigma$ and $\varepsilon$ remain proportional.
Poisson's ratio
Under uniaxial tension, longitudinal elongation is accompanied by transverse contraction. Poisson's ratio is defined as $\nu=-\varepsilon_{\perp}/\varepsilon_{\parallel}$, where $\varepsilon_{\perp}$ is transverse strain and $\varepsilon_{\parallel}$ is longitudinal strain.
Shear modulus
The shear modulus $G$ characterizes material stiffness in shear. For a linearly elastic isotropic material, the elastic constants are related by $G=E/[2(1+\nu)]$.
Engineering application
$E$ is used in tension, compression, and bending calculations; $G$ is used in shear and torsion; and $\nu$ is needed to describe the coupling between longitudinal and transverse strains.