Optimal Bounds on Plastic Deformations for Bodies Constituted of Temperature-Dependent Elastic Hardening Material

Abstract

Bounds are investigated on the plastic deformations in a continuous solid body produced during the transient phase by cyclic loading not exceeding the shakedown limit. The constitutive model employs internal variables to describe temperature-dependent elastic-plastic material response with hardening. A deformation bounding theorem is proved. Bounds turn out to depend on some fictitious self-stresses and mechanical internal variables evaluated in the whole structure. An optimization problem, aimed to make the bound most stringent, is formulated. The Euler-Lagrange equations related to this last problem are deduced and they show that the relevant optimal bound has a local character, i.e., it depends just on some fictitious plastic deformations produced in the same region of the body where the bounded real plastic deformations are considered. The bounding technique is also generalized to the case of loads arbitrarily varying in a given domain. An application is worked out.