On the characteristic equations of elasto-plastic flow

Three dimensional characteristic surfaces (slip surfaces) of elasto-plastic Navier's equations and the criteria for their existence are discussed, and the solutions are also applied to two dimensional cases. By making use of isotropic yield function, the following results are proved. If, and only if the plastic/elastic moduli ratio is zero and Det$\text{(φ}{}_{\mathrm{ij}}\text{)=0,(φ}{}_{\mathrm{ij}}\text{=}\text{?φ}\text{?σ}{}_{\mathrm{ij}}$, φ: yield function,σ_ij: stress tensor), characteristic surfaces exist. There are two and only two characteristic surface elements at each point, and they are identical with the surfaces of maximum shearing stress.