Consistent shakedown theorems for materials with temperature dependent yield functions

The (elastic) shakedown problem for structures subjected to loads and temperature variations is addressed in the hypothesis of elastic-plastic rate-independent associative material models with temperature-dependent yield functions. Assuming the yield functions convex in the stress/temperature space, a thermodynamically consistent small-deformation thermo-plasticity theory is provided, in which the set of state and evolutive variables includes the temperature and the plastic entropy rate. Within the latter theory the known static (Prager's) and kinematic (König's) shakedown theorems - which hold for yield functions convex in the stress space - are restated in an appropriate consistent format. In contrast with the above known theorems, the restated theorems provide dual lower and upper bound statements for the shakedown limit loads; additionally, the latter theorems can be expressed in terms of only dominant thermo-mechanical loads (generally the vertices of a polyhedral load domain in which the loadings are allowed to range). The shakedown limit load evaluation problem is discussed together with the related shakedown limit state of the structure. A few numerical applications are presented. © 2000 Elsevier Science Ltd. All rights reserved.