显式方法精确模拟形状记忆合金循环荷载下的变形行为

本文提出全新的有限弹塑性J2流方程,用来显式、精确地模拟SMAs（形状记忆合金）材料在循环加载-卸载条件下从塑性逐渐转变为伪弹性的变形行为．首先,改进流动法,使得本构方程耦合屈服中心的移动和屈服面的增大,并改进背应力演化方程,使模型可以产生强烈的包辛格效应,从理论上具备模拟SMAs独特变形行为的能力;其次,构造全过程下的统一硬化函数显式表达式,代入本构方程后能得到符合要求的形函数;再次,利用选定的数据点构造统一光滑的上屈服函数,再利用上下屈服应力之间的一种线性关系,推导得到下屈服阶段的形函数;最后,只需要给定一个参数就可以得到单个循环结果,利用拉格朗日插值方法构建参数随循环次数变化的函数,就可以模拟任意循环荷载下的变形行为．通过模型结果和实验数据对比证明新方法的有效性．

Explicitly,Exactly Modelling Deformation Behaviour of SMAs under Cyclic Loading

New finite elastoplastic J2-flow equations are proposed to explicitly, exactly simulate the continuous transition of deformation behavior of shape memory alloys (SMAs) from plasticity to pseudo-elasticity under the multiple loading-unloading cycles. First, the flow rule is modified to incorporate the moving of yield center and the expanding of the yield surface into the constitutive law. Then, the evolution equation of the back stress is improved to produce intense Bauschinger effect and enable the model to simulate the unique deformation behavior of SMAs. Second, the hardening function in whole range is constructed, and substituted into the constitutive equations to obtain the qualified shape functions. Third, smooth and unified shape functions for the upper yield stage are constructed based on the chosen data. The shape functions for the lower yield stage can also be deduced according to the linear relationship between the upper yield stress and the lower yield stress. Lastly, the single hysteresis loop can be obtained by giving only one parameter value. Through constructing the function whose parameter varies with the number of cycle using the Lagrange interpolation method, we can simulate the deformation behaviors under arbitrary cyclic loading. The model is validated through comparison between the model results and the experimental data.