Based on the Gurson–Tvergaard–Needleman (GTN) model, a constitutive relationship considering both the effects of strain hardening and hydrostatic stress for porous shape memory alloys (SMAs) is proposed. To capture the relationship between microscopic and mesoscopic behaviors, a representative volume element (RVE) containing an array of spherical voids is presented. In this paper, an approximate solution including strain hardening exponent [Formula: see text] is deduced by considering the porous SMA as a two phase composite with the SMA matrix and the second phase representing voids. The model parameters, [Formula: see text] and [Formula: see text], accounting for interactions between voids are investigated to take into account their influences on strain hardening, critical phase transformation stress and yield surface. In addition, the evolution equations of phase transformation are derived and then applied to the simulation of porous Ni–Ti SMAs with a porosity of 13%. Using the calibrated GTN model parameters, the critical phase transformation stress closer to experimental data is obtained. The predictions of stress–strain curve by the proposed constitutive model are found to be in excellent agreement with published experimental data and finite element results. The results prove that the model is capable of reproducing the features of porous SMAs such as superelasticity, tensile-compressive asymmetry and internal loops under uniaxial even combined loading conditions. A conclusion is drawn that the present constitutive relationship is powerful and useful for the analysis of porous SMAs.

中文翻译：

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在等温条件下使用 Gurson-Tvergaard-Needleman 模型对多孔形状记忆合金进行本构建模

基于 Gurson-Tvergaard-Needleman (GTN) 模型，提出了考虑应变硬化和静水应力对多孔形状记忆合金 (SMA) 的影响的本构关系。为了捕捉微观和中观行为之间的关系，提出了一个包含球形空隙阵列的代表性体积元 (RVE)。在本文中，通过将多孔 SMA 视为具有 SMA 基体和代表空隙的第二相的双相复合材料，推导出了包括应变硬化指数 [公式：见正文] 的近似解。模型参数 [公式：参见文本] 和 [公式：参见文本] 考虑了空隙之间的相互作用，以考虑它们对应变硬化、临界相变应力和屈服面的影响。此外，推导了相变的演化方程，然后将其应用于孔隙率为 13% 的多孔 Ni-Ti SMA 的模拟。使用校准后的GTN模型参数，得到更接近实验数据的临界相变应力。发现所提出的本构模型对应力-应变曲线的预测与已发表的实验数据和有限元结果非常吻合。结果证明，该模型能够在单轴甚至组合加载条件下再现多孔SMA的超弹性、拉伸-压缩不对称和内环等特征。得出的结论是，目前的本构关系对于分析多孔 SMA 是强有力的和有用的。