Thermo-coupled elastoplasticity models with asymptotic loss of the material strength

• Free rate-independent elastoplastic equations with thermo-coupled effects.
• No reference to usual yield condition and loading–unloading conditions.
• Smooth transition from elastic to plastic state.
• Fatigue, fracture and failure are incorporated into inherent constitutive features.

Rate-independent finite elastoplastic equations with thermo-coupled effects are proposed to bypass the yield condition and loading–unloading conditions. These new equations are shown to be more realistic and of much simpler structure than classical equations. In a sense of thermodynamic consistency the strength property of elastoplastic solids is then studied from the standpoint of stress-bearing capacity. It is shown that asymptotic loss of the strength may be derived directly from elastoplastic equations, thus leading to the finding of a noticeable phenomenon, namely, asymptotic vanishing of the stress concurrent with developing elastoplastic flow. It is indicated that this finding may suggest a natural constitutive characterization of fatigue, fracture and failure as certain limiting cases of elastoplastic behavior. Simple models with asymptotic loss of the strength are constructed as examples of potential practical applications.