Supplementary Materials

See the supplementary material for the input parameters for the phase-field model; the temporal evolution of the phasefield variable (η) representing electrical breakdown under an applied electric field of 240 kV/mm, simulated for different driving forces: electric field only, thermal field only, mechanical field only, coupled thermo-mechanical fields, and coupled electro-thermo-mechanical fields; the electrical breakdown phase under an applied electric field of 240 kV/mm at t∗ = 2 for composite systems with different random distributions of BTO particles with diameters of 20 nm and 30 nm.