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Solid Mechanics: Hooke's Law
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| Isotropic Definition |
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| Most metallic alloys and thermoset polymers are
considered isotropic, where by
definition the material properties are independent of direction.
Such materials have only 2 independent variables (i.e. elastic
constants) in their stiffness and compliance matrices, as opposed to
the 21 elastic constants in the general anisotropic
case.
The two elastic constants are usually expressed as the Young's modulus E and the Poisson's ratio n. However, the alternative elastic constants K (bulk modulus) and/or G (shear modulus) can also be used. For isotropic materials, G and K can be found from E and n by a set of equations, and vice-versa. |
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| Hooke's Law in Compliance Form |
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| Hooke's law for isotropic materials in compliance matrix form is given by,
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| Hooke's Law in Stiffness Form |
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| The stiffness
matrix is equal to the inverse of the compliance matrix,
and is given by,
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