It is challenging to precisely model the complicated plastic deformation of metals, including anisotropy in strength and plastic deformation, strength differential effect, anisotropic hardening, etc. A new approach is proposed to extend anisotropic yield functions into asymmetric ones by introducing a Lode dependent function. The approach is applied to the Hill48 function with a Lode-dependent function in a form of the normalized third stress invariant. The proposed Lode-dependent anisotropic-asymmetric (LAA) is applied to characterize the anisotropic hardening behaviors under both tension and compression of QP1180, DP980, AA2008 T4 and $\alpha$-Ti to verify its performance. The convexity of yield surface evolution with plastic deformation is investigated by a geometry-inspired numerical convex analysis method. The application shows that the proposed LAA function precisely characterizes the anisotropy in tension and compression and its evolution with plastic deformation. It is therefore suggested to model the anisotropic-asymmetric plastic behavior with its applications to metal forming.

精确模拟金属的复杂塑性变形具有挑战性，包括强度和塑性变形的各向异性、强度差异效应、各向异性硬化等。提出了一种通过引入 Lode 相关函数将各向异性屈服函数扩展到不对称屈服函数的新方法。该方法以归一化第三应力不变量的形式应用于具有 Lode 相关函数的 Hill48 函数。所提出的 Lode 依赖性各向异性不对称 (LAA) 用于表征 QP1180、DP980、AA2008 T4 和$\alpha$-Ti 来验证其性能。通过几何启发的数值凸分析方法研究屈服面随塑性变形演化的凸性。应用表明，所提出的 LAA 函数精确地描述了拉伸和压缩的各向异性及其随塑性变形的演变。因此，建议将各向异性不对称塑性行为及其在金属成型中的应用进行建模。