Inelastic responses of a two-bar system with temperature-dependent elastic modulus under cyclic thermomechanical loadings

This paper is concerned with the elastic plastic response of a two-bar system with temperature-dependent elastic coefficients under cyclic thermomechanical loadings. Such materials are characterized by lack of results concerning the asymptotic behaviors and conditions for shakedown occurrence. This study shows that the considered simple structure is sufficiently complex to experience different periodic long-term behaviors as in classical elastoplasticity. In order to understand how Melan–Koiter method works for such materials, the evolution of the structure’s response until the stabilization of the plastic strain (‘shakedown’) or the asymptotic dissipative behavior (‘alternating plasticity’ or ‘ratcheting’) is analytically addressed and the Bree diagram is then constructed. The main result of this work is that the residual stress and strain fields are time-dependent even when shakedown occurs. Besides, we proved that Halphen’s conjecture (Halphen, 2005) giving a sufficient condition for shakedown occurrence is not a necessary condition. Finally, numerical results performed by an incremental finite element procedure are presented.