This work addresses the numerical simulation of transformation plasticity by using a numerical scheme based on the fast Fourier transform (FFT). A two-phase material with isotropic thermo-elastoplastic phases is considered. Together with prescribed transformation kinetics, this permits to describe the plasticity induced by the accommodation of the volume change accompanying the phase transformation (Greenwood–Johnson mechanism). We consider random distributions of $\alpha$-phase nuclei within a homogeneous $\gamma$-phase matrix, with an isotropic growth law of the nuclei. The numerical results are compared to a recently proposed limit-analysis-based theory (El Majaty et al., 2018), which permits in particular to account for a nonlinear dependence of the “transformation plastic strain” with the stress applied. A very good agreement between the FFT simulations and the theory is obtained, for uniaxial and multiaxial loadings, over a wide range of stresses applied.

这项工作通过使用基于快速傅立叶变换（FFT）的数值方案来解决相变塑性的数值模拟问题。考虑具有各向同性热弹塑性相的两相材料。连同规定的转变动力学一起，这可以描述由于伴随相变而发生的体积变化的调节而引起的可塑性（格林伍德-约翰逊机理）。我们考虑随机分布$\alpha$均质内的相核 $\gamma$相矩阵，具有各向同性的原子核生长规律。将数值结果与最近提出的基于极限分析的理论（El Majaty等人，2018）进行了比较，该理论尤其考虑了“变形塑性应变”与所施加应力之间的非线性相关性。对于单轴和多轴载荷，在广泛的应力范围内，FFT模拟与理论之间取得了很好的一致性。