Subsequent yield surfaces of ductile solids, pre-strained in shear and/or tension, exhibit various characteristic features that depend on the proof strain used to detect yield. These features include kinematic hardening when the proof strain denoting yield is low, isotropic hardening when it is high, formation of a ‘nose’ in the loading direction and flattening of the rear part of the yield surface. With the aid of a computational homogenisation scheme that allows application of arbitrary macro stress or macro deformation gradient to a unit cell, we show that essential features of the subsequent yield surfaces owe their origin to the extent of plasticity accumulated within the unit cell. For instance, a simple unit cell containing a spherical void, where the void serves to create a heterogenous distribution of plastic strain, suffices to computationally reproduce the experimentally observed features. Moreover, in contrast to experiments which generally allow plotting of the yield surface in a normal stress – shear stress plane, the computational scheme allows fuller exploration of the subsequent macro yield surface in the macro stress space. We find that what seems to be a translation and distortion of the yield surface in experiments, is actually most pronounced near some critical octahedral planes characterised by levels of triaxiality induced by the pre-straining process. The evolution of the yield surface in regions where the triaxiality is higher is considerably different. Moreover, as homogeneous yielding is approached with loading of the unit cell, the material seems to forget the nature of the pre-straining process and undergoes isotropic hardening.

随后在剪切和/或拉力作用下应变的易延展固体的屈服面表现出各种特征，这些特征取决于用于检测屈服的屈服应变。这些特征包括：当屈服应变表示屈服力低时进行运动硬化，当屈服应变表示屈服力高时则进行各向同性淬火，在载荷方向上形成“鼻子”，并使屈服面的后部变平。借助于允许对单元晶胞施加任意宏观应力或宏观变形梯度的计算均质化方案，我们表明，后续屈服面的基本特征归因于其在晶胞内积累的可塑性程度。例如，包含球形空隙的简单晶胞，其中空隙用于产生塑性应变的异质分布，足以通过计算重现实验观察到的特征。此外，与通常允许在法向应力-剪切应力平面上绘制屈服面的实验相反，该计算方案可以在宏观应力空间中更全面地探索随后的宏观屈服面。我们发现，在实验中似乎是屈服面的平移和变形，实际上在某些临界八面体平面附近最为明显，该八面体平面的特征是预应变过程引起的三轴性水平。在三轴度较高的区域中，屈服面的演变差异很大。此外，随着单位晶胞的加载接近均匀屈服，该材料似乎忘记了预应变过程的性质，并经历了各向同性的硬化。