A bounding technique for plastic deformations

Abstract

On the grounds of the known proportionality between the kinematical part of the solution of the Euler-Lagrange equations relative to the shakedown load factor problem for an elastic perfectly plastic solid subjected to cyclic loads and the gradient of the kinematical part of the elastic-plastic steady-state response of the solid to cyclic loads at the shakedown limit, a special bounding technique is developed. Such technique consists of computing a bound on the proportionality factor between the two kinematical solutions and, consequently, bounds on any measure of real plastic deformation produced by cyclic loads slightly above the shakedown limit. The technique is then generalized to the case of loads arbitraily varying within a given load domain. Some computational aspects are also discussed. Two examples solved in analytic form and one numerical application conclude the paper.