非线性随动强化条件下的安定定理

Shakedown theorems for elastic plastic nonlinear kinematic-hardening solids

基于经典的安定理论与随动强化模型的一般性质,将结构在强化过程中的背应力计入Von Mises屈服准则,建立了随动强化条件下结构的静力安定定理;将背应力与对应的塑性应变率的点积在一个载荷循环内的积分计入塑性耗散功,建立了随动强化条件下结构的机动安定定理,扩展了经典安定理论的应用范围。针对两种定理的存在格式进行了理论证明,并以推论形式给出了结构在随动强化条件下静力安定和机动安定另外两种存在格式。结果表明,随动强化材料的安定状态和安定极限不受强化过程的影响,只取决于材料的初始屈服应力和最终屈服应力。

Based on classical shakedown theorems,the general nonlinear kinematic-hardening is considered,and the back stress of particular hardening law to the corresponding plastic deformation is included.Firstly,the back stress is included to Von Mises yield criterion,then static theorem for elastic-plastic nonlinear kinematic-hardening solids are derived.Secondly,the dot matrix of back stress and plastic strain rate is added to dissipation function,then kinematic theorem for elastic-plastic nonlinear kinematic hardening solids are derived.The classical shakedown theorems are extended to nonlinear kinematic-hardening bodies,and two corollaries are given based on shakedown theorems for nonlinear kinematic-hardening bodies.The theorems reveal that the shakedown of structures is not affected by the particular form of the hardening curve,but just by the initial and ultimate yield stresses.