where J is the induced electric current, Je includes external current sources that do not result from the material conductivity (such as thermoelectric currents), D is the electric displacement field, and Qj is a current source term. Both Qj and Je are usually zero for piezoresistive devices.

In the stationary or quasistatic case, the electric current is related to the electric field, E, by the constitutive relation:

where σ(c) is the conductivity tensor.

Relating E and D to the electric potential (E=-∇V, D=ε0ε(r)E, where ε0 is the permittivity of free space and ε(r) is the relative permittivity tensor) gives:

where the operator ∇t represents the tangential derivative along the thin layer surface. Equation 6-4 and Equation 6-5 form the basis of the Electric Currents interface.

Since the equations of piezoresistivity are by convention formulated in the resistivity form, Equation 6-1 must be inverted to give:

Although this expression appears cumbersome, it is required in this form for the general case where the conductivity and change in resistivity are nonsymmetric tensor quantities. For convenience, the tensor σ(c, eff) is defined as:

The Piezoresistivity, Domain Currents Interface solves a modified form of Equation 6-4 on the domain level:

while The Piezoresistivity, Boundary Currents Interface and The Piezoresistivity, Shell Interface solve a modified form of equation Equation 6-5 on the boundary level:

where σ(c, eff) is computed from Equation 6-7 and from the definition of Δρ given in Equation 6-2.