A fully analytical framework of yield criterion is constructed under non-associated flow rule to describe asymmetric yielding and anisotropic hardening based on the concept of shape functions. For the yield function, eight parameters are identified by employing the corresponding tensile and compressive hardening functions along the four directions, i.e., uniaxial directions along 0°, 45°, 90° in relation to the rolling direction and equi-biaxial direction. This function can describe continuous non-uniform evolution of yield loci during anisotropic hardening. Besides, a new analytical plastic potential function is also developed to predict the asymmetric R-values along uniaxial tension and compression. Subsequently, a simpler curvature control method is proposed to control the curvature of yield surface, especially suitable for materials with large anisotropy. The effectiveness and accuracy of the proposed criterion are validated with HCP, FCC and BCC crystal structure materials for predicting asymmetric uniaxial yield stress curves, R-value curves, and non-uniform evolution of yield loci. The validations indicate that this new criterion has concise mathematical structure and great capability of asymmetry description. Eventually, an extension method for the yield criterion from 2D to 3D is discussed in the reasonability and incompressibility.

基于形函数的概念，在非关联流动规则下构建了一个完整的屈服准则分析框架来描述非对称屈服和各向异性硬化。对于屈服函数，通过沿四个方向使用相应的拉伸和压缩硬化函数来确定八个参数，即，相对于轧制方向和等双轴方向沿0°、45°、90°的单轴方向。该函数可以描述各向异性硬化过程中屈服轨迹的连续非均匀演化。此外，还开发了一种新的分析塑性势函数来预测沿单轴拉伸和压缩的不对称 R 值。随后，提出了一种更简单的曲率控制方法来控制屈服面的曲率，特别适用于各向异性较大的材料。所提出准则的有效性和准确性通过 HCP、FCC 和 BCC 晶体结构材料验证，用于预测不对称单轴屈服应力曲线、R 值曲线和屈服轨迹的非均匀演化。验证表明该新准则具有简洁的数学结构和强大的非对称描述能力。最后，在合理性和不可压缩性方面讨论了屈服准则从2D到3D的扩展方法。验证表明该新准则具有简洁的数学结构和强大的非对称描述能力。最后，在合理性和不可压缩性方面讨论了屈服准则从2D到3D的扩展方法。验证表明该新准则具有简洁的数学结构和强大的非对称描述能力。最后，在合理性和不可压缩性方面讨论了屈服准则从2D到3D的扩展方法。