Stress and strain

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Hooke’s law gives the relationship between force, F, the extension, x, of an elastic object like a spring and the material’s spring constant, k:

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Tensile stress and strain

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Tensile stress = perpendicular force / area

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Tensile strain = change in length / original length

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These are combined into Young’s modulus = stress / strain

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This is the gradient of a graph of stress against strain up until the limit of proportionality. The area under this graph is the energy stored.

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The limit of proportionality is the point at which Hooke’s law stops applying. The elastic limit is the point at which the object won’t return to its original length. The yield point is the point at which length starts to increase more with the same force. The breaking point is when the material breaks.

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There are other types of stress and strain:

Bulk stress and strain

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Bulk stress = change in pressure

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Bulk strain = change in volume / original volume

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Shear stress and strain

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Shear stress = parallel force / area

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Shear strain = change in width / height

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In both cases the modulus is stress over strain. Bulk modulus has the symbol B and shear modulus has symbol S.

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Shear stress defines viscosity, η, which is a measure of how much a top layer of fluid moves compared to a bottom layer of fluid (Δu is the difference in speeds at the top and bottom and Δz is the height):

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Back to Physics: Contents: Mechanics

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