  We present results for the steady-state nonlinear response of a $d_{x^2-y^2}$
superconducting film connected to normal-metal reservoirs under voltage bias,
allowing for a subdominant $s$-wave component appearing near the interfaces.
Our investigation is based on a current-conserving theory that
self-consistently includes the non-equilibrium distribution functions, charge
imbalance, and the voltage-dependencies of order parameters and scalar impurity
self-energies. For a pure $d$-wave superconductor with [110] orientation of the
interfaces to the contacts, the conductance contains a zero-bias peak
reflecting the large density of zero-energy interface Andreev bound states.
Including a subdominant $s$-wave pairing channel, it is in equilibrium
energetically favorable for an $s$-wave order parameter component
$\Delta_\mathrm{s}$ to appear near the interfaces in the time-reversal symmetry
breaking combination $d+is$. The Andreev states then shift to finite energies
in the density of states. Under voltage bias, we find that the non-equilibrium
distribution in the contact area causes a rapid suppression of the $s$-wave
component to zero as the voltage $eV\rightarrow\Delta_\mathrm{s}$. The
resulting spectral rearrangements and voltage-dependent scattering amplitudes
lead to a pronounced non-thermally broadened split of the zero-bias conductance
peak that is not seen in a non-selfconsistent Landauer-B\"uttiker scattering
approach.
