The contact stress within LLZO was estimated using finite element analysis in ABAQUS package. For tungsten contact, the full elasto-plastic constitutive law of W was adopted from the literature and considered in the model (Young's modulus E = 400 GPa, the initial yield stress = 1.42 GPa, ultimate tensile strength = 1.73 GPa). For LLZO, we assumed a linear elastic-perfect plastic constitutive law with E = 150 GPa, v = 0.24 and an assumed yield strength of 4.5 GPa.