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本文提出了基于俞茂宏统一强度理论的双剪统一相关和非相关流动的弹塑性本构模型，并给出了该统一弹塑性本构模型的有限元实施方法。重点讨论了所谓“奇异屈服面”奇异性的处理方法，定义了两类不同类型的奇异形式，给出了它们的不同处理方法。该方法既直观、简单又便于有限元的实施，它对于其它类型“奇异屈服面”角点奇异性的处理同样适用。应用基于该统一弹塑性本构模型的有限元程序ＵＥＰＰ（ＵｎｉｆｉｅｄＥｌａｓｔｏ－ＰｌａｓｔｉｃｆｉｎｉｔｅｅｌｅｍｅｎｔＰｒｏｇｒａｍ），验证了作者提出的双剪统一弹塑性本构模型及其实施方法的正确性。统一强度理论和双剪统一弹塑性本构模型可以广泛应用于各种土木、机械、航空和岩土工程的结构分析。
In this paper, an elasto-plastic constitutive model based on Yu Maohong’s unified strength theory for double-shear unified correlation and non-correlation flow is proposed, and a finite element implementation method for the unified elasto-plastic constitutive model is given. The method of dealing with the singularity of the so-called “singular yield surface” is mainly discussed. Two different types of singular forms are defined, and their different processing methods are given. This method is intuitive, simple and easy to implement with finite element. It is also applicable to the treatment of singular singularities of other types of singular yield surface. The finite element program UEPP (Unified Elasto-Plastic finite Element Program) based on the unified elasto-plastic constitutive model was applied to verify the correctness of the proposed twin shear unified elastoplastic constitutive model and its implementation method. The unified strength theory and the twin shear unified elasto-plastic constitutive model can be widely applied to the structural analysis of various civil, mechanical, aerospace and geotechnical engineering.