A fast and robust stress-integration algorithm is the key to full exploitation of advanced anisotropic yield functions in computational mechanics. Poor global convergence of a direct application of the Newton-Raphson scheme has been rectified by applying line search strategies during the Newton iterations. In this work the line-search approach is further improved by a better first guess. The new algorithm is implemented into a user-defined material subroutine (UMAT) in a finite-element (FE) software and tested. The implementation is made easier and more efficient by a new advantageous vector/matrix notation for symmetric second- and fourth-order tensors, which is the second result of this work. Benefits of this notation are discussed with respect to formulation of continuum-plasticity models as well as their implementations. FE simulations were run to demonstrate the performance of the new implementation, which is available as open-source software via GitLab repository (see Appendix). The new return-mapping algorithm implementation runs equally fast and robust as the simple von Mises and Hill standard implementations in the Abaqus/Standard software. This enables full exploitation of advanced yield functions as the new standard in industrial FE applications.

快速且稳健的应力积分算法是充分利用计算力学中先进的各向异性屈服函数的关键。通过在牛顿迭代期间应用线搜索策略，已经纠正了直接应用 Newton-Raphson 方案的全局收敛性差。在这项工作中，通过更好的初步猜测进一步改进了线搜索方法。新算法在有限元 (FE) 软件中实现到用户定义的材料子程序 (UMAT) 中并进行测试。通过用于对称二阶和四阶张量的新的有利向量/矩阵表示法，实现变得更容易和更高效，这是这项工作的第二个结果。讨论了这种表示法的好处是关于连续可塑性模型的制定及其实现。运行 FE 模拟以演示新实现的性能，该实现可通过 GitLab 存储库作为开源软件使用（参见附录）。新的返回映射算法实现与 Abaqus/Standard 软件中简单的 von Mises 和 Hill 标准实现一样快速和稳健。这使得可以充分利用先进的良率函数作为工业 FE 应用的新标准。