Semi-implicit type cutting plane method (CPM) and fully implicit type closest point projection method (CPPM) are the two most widely used frameworks for numerical stress integration. CPM is simple, easy to implement and accurate up to first order. CPPM is unconditionally stable and accurate up to second order though the formulation is complex. Therefore, this study aims to develop a less complex and accurate stress integration method for complex constitutive models.,Two integration techniques are formulated using the midpoint and Romberg method by modifying CPM. The algorithms are implemented for three different classes of soil constitutive model. The efficiency of the algorithms is judged via stress point analysis and solving a boundary value problem.,Stress point analysis indicates that the proposed algorithms are stable even with a large step size. In addition, numerical analysis for solving boundary value problem demonstrates a significant reduction in central processing unit (CPU) time with the use of the semi-implicit-type midpoint algorithm.,Traditionally, midpoint and Romberg algorithms are formulated from explicit integration techniques, whereas the present study uses a semi-implicit approach to enhance stability. In addition, the proposed stress integration algorithms provide an efficient means to solve boundary value problems pertaining to geotechnical engineering.

中文翻译：

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单一硬化土本构模型的半隐式中点和 Romberg 应力积分算法的开发

半隐式切割平面法（CPM）和全隐式最近点投影法（CPPM）是两种最广泛使用的数值应力积分框架。CPM 简单、易于实施且精确到一阶。尽管公式复杂，但 CPPM 无条件稳定且精确到二阶。因此，本研究旨在为复杂的本构模型开发一种不太复杂和准确的应力积分方法。通过修改 CPM，使用中点和 Romberg 方法制定了两种积分技术。该算法针对三种不同类别的土壤本构模型实施。通过应力点分析和求解边界值问题来判断算法的效率。应力点分析表明，即使在大步长下，所提出的算法也是稳定的。此外，求解边界值问题的数值分析表明，使用半隐式中点算法显着减少了中央处理器 (CPU) 时间。传统上，中点和 Romberg 算法是通过显式积分技术制定的，而本研究使用半隐式方法来增强稳定性。此外，所提出的应力积分算法提供了一种有效的方法来解决与岩土工程有关的边界值问题。中点和 Romberg 算法是从显式积分技术制定的，而本研究使用半隐式方法来增强稳定性。此外，所提出的应力积分算法提供了一种有效的方法来解决与岩土工程有关的边界值问题。中点和 Romberg 算法是从显式积分技术制定的，而本研究使用半隐式方法来增强稳定性。此外，所提出的应力积分算法提供了一种有效的方法来解决与岩土工程有关的边界值问题。