Defining a Piezoresistive Material
A piezoresistive material undergoes a change in its electrical resistivity when it is stressed. This coupling between stress and electrical resistivity is the material's piezoresistivity property. The electrical response of the material is also defined in terms of electrical resistivity properties when the material is unstressed.
The piezoresistive effect can be defined by
where
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is the mechanical stress tensor;
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the material’s piezoresistivity coefficient tensor; and
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is a tensor that represents the relative change in the electrical resistivity with stress.
The material’s electrical resistivity when stressed is defined by
where
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is the material’s electrical resistivity tensor when it is in an unstressed state; and
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is the Kronecker delta.