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The complementary variational problems for finite plasticity with strainhardening effect are developed in this paper based on the theory of convex analysis. A new lower bound theorem for the load intensity factor, in which the plastic yield condition is relaxed by a complementary plastic superpotential, is proved. A simple illustrative example is worked out.doi:10.1090/qam/1012265 fatcat:xwk7q5h35fhs5l3jy44qsurwv4