形状记忆合金相变过程三维大变形有限元模拟

形状记忆合金（SMA）一直被作为智能材料开发，并被用于阻尼器、促动器和智能传感器元件．形状记忆合金（SMA）的一项重要特性，是它具有恢复在机械加卸载周期下产生的大变形而不表现出永久变形的能力．该文旨在介绍一种由应力产生的相变且可以描述马氏体和奥氏体之间的超弹性滞回环现象本构方程．形状记忆合金的马氏体系数假设为应力偏张量的函数,因此形状记忆合金在相变过程中锁定体积．本构模型是在大变形有限元的基础上执行的，采用了现时构型Lagrange大变形算法．为了方便地使用Cauchy应力和线性应变本构关系，使用了与旋转无关的Jaumann应力增率计算应力．数值分析结果表明，相变引起的超弹性滞回环可以有效地通过该文提出的本构方程和大变形有限元模拟．

Three Dimensional Large Deformation Analysis of Phase Transformation in Shape Memory Alloys

Shape memory alloys (SMAs) have been explored as smart materials and used as dampers, actuator elements and smart sensors.An important character of SMAs is its ability to recover all of its large deformations in mechanical loading-unloading cycles, without showing permanent deformation.A stress-induced phenomenological constitutive equation for SMAs, which can be used to describe the superelastic hysteresis loops and phase transformation between martensite and austenite was presented.The martensite fraction of SMAs was assumed to be dependent on deviatoric stress tensor.Therefore phase transformation of shape memory alloys was volume preserving during the phase transformation.The model was implemented in large deformation finite element code and cast in the updated Lagrangian scheme.In order to use Cauchy stress and the linear strain in constitutive laws, a frame indifferent stress objective rate has to be used and the Jaumann stress rate was used. The results of the numerical experiments conducted show that the superelastic hysteresis loops arising with the phase transformation can be effectively captured.