where ρ is the resistivity and
Δρ is the induced change in the resistivity. In the general case both
ρ and
Δρ are rank 2 tensors (matrices). The change in resistance is related to the stress,
σ (for the piezoresistance form of the equations), or the strain,
ε (for the elastoresistance form of the equations), by the constitutive relationship:
where Π is the piezoresistance tensor (SI unit: Pa
−1Ωm) and
M is the elastoresistance tensor (SI unit:
Ωm). Both of these quantities are material properties.
Π and
M are in this case rank 4 tensors; however, they can be represented as matrices if the resistivity, stress, and strain are converted to vectors within a reduced subscript notation.