Toward directly simulating pseudo-elastic effects of shape memory alloys, new elastoplastic equations of von Mises type are proposed by correlating the yield surface radius with the yield surface center, thus establishing a new elastoplasticity model characterized by three coupled quantities for isotropic and anisotropic hardening. Within the framework of conventional macroscopic elastoplasticity, it is demonstrated that the new model can exactly reproduce pseudo-elastic hysteresis effects of shape memory alloys, with no need to characterize any microstructural features of solid–solid phase transitions. To this end, explicit expressions for the three hardening quantities introduced are presented in terms of two single-variable functions. Then, exact closed-form solutions are obtained for the uniaxial stress–strain responses in a loading and a subsequent unloading process, and such responses are shown to give rise to a hysteresis loop shaped just by the foregoing two single-variable functions. As such, hysteresis loops of arbitrary shapes can be simulated in a straightforward and accurate manner simply prescribing two single-variable functions shaping such loops. For the first time, cumbersome and time-consuming procedures both for conducting statistical averaging schemes and for identifying numerous unknown parameters may be bypassed with broad applicability.

为了直接模拟形状记忆合金的伪弹性效应，通过将屈服面半径与屈服面中心相关联，提出了新的 von Mises 型弹塑性方程，从而建立了以各向同性和各向异性硬化三个耦合量为特征的新弹塑性模型。在常规宏观弹塑性的框架内，证明了新模型可以准确地再现形状记忆合金的伪弹性滞后效应，而无需表征任何固-固相变的微观结构特征。为此，引入的三个硬化量的显式表达式以两个单变量函数的形式呈现。然后，对于加载和随后的卸载过程中的单轴应力-应变响应，获得了精确的闭合形式的解，并且这种响应显示出仅由上述两个单变量函数形成的滞后回线。因此，任意形状的磁滞回线可以以直接和准确的方式进行模拟，只需指定两个单变量函数来塑造这种回线。第一次，可以绕过用于执行统计平均方案和识别大量未知参数的繁琐和耗时的程序，并具有广泛的适用性。任意形状的磁滞回线可以以直接和准确的方式进行模拟，只需指定两个单变量函数来塑造这种回线。第一次，可以绕过用于执行统计平均方案和识别大量未知参数的繁琐和耗时的程序，并具有广泛的适用性。任意形状的磁滞回线可以以直接和准确的方式进行模拟，只需指定两个单变量函数来塑造这种回线。第一次，可以绕过用于执行统计平均方案和识别大量未知参数的繁琐和耗时的程序，并具有广泛的适用性。