Fundamental properties of elasto-plastic matrix and existence and uniqueness of elasto-plastic stress and displacement

Based on the assumption that the yield criterionF(,)=0 is a differentiable surface in stress space and by starting from a specially defined real Euclidean space, the fundamental properties of the elasto-plastic matrix in the incremental theory of plasticity is discussed in detail. By using these results, a convex analysis is made to prove the existence and uniqueness of 1) the distribution of incremental elasto-plastic stress for work-hardening materrials; 2) the displacement distribution for work-hardening materials. Material isotropy is assumed in all discussions of relevant problems.