In the paper, a pragmatic approach to finding the dual formulation for isotropic perfectly plastic materials given a dissipation potential dependent on three cylindrical invariants and involving the Ottosen shape function is proposed and illustrated by examples. The main goal is to provide instructions on how to perform the Legendre transformation used when passing from a dissipation potential to its conjugate yield condition and offer some suggestions regarding calibration for particular potentials dependent on the trace of the strain rate tensor and the product of the norm of its deviator and the Ottosen shape function, which covers a wide class of engineering materials. The classic framework for constitutive modelling of thermodynamically consistent materials within the small deformation theory is used. First, general formulae connecting a dissipation potential dependent on three invariants of the strain rate tensor to the coupled yield condition are derived. Then, they are narrowed down for the aforementioned case of dissipation functions dependent on the Lode angle in a way proposed by Ottosen. Finally, three examples are given involving classical potentials: Beltrami’s, Drucker–Prager’s and Mises–Schleicher’s generalised potential using the shape function. Detailed calculations exposing the introduced technique are performed. Also, a method of the calibration of such potentials leading to explicit mathematical formulae is demonstrated, based on the typical tests located on the tension and compression meridians.

在本文中，提出了一种实用的方法来寻找各向同性完美塑性材料的对偶公式，并给出耗散势取决于三个圆柱不变性并涉及奥托森形状函数的例子，并通过示例进行说明。主要目标是提供有关如何执行从耗散电势到其共轭屈服条件时使用的勒让德变换的说明，并根据应变率张量的轨迹和范数的乘积，针对特定电势的校准提供一些建议。它的偏角和奥托森形状函数，涵盖了广泛的工程材料。使用小变形理论中热力学一致性材料的本构模型的经典框架。第一，推导了将依赖于应变率张量的三个不变量的耗散电势与耦合屈服条件联系起来的一般公式。然后，对于上述取决于洛德角的耗散函数的情况，以Ottosen提出的方式将其范围缩小。最后，给出了三个涉及经典势的示例：Beltrami势，Drucker-Prager势和Mises-Schleicher势函数使用形状函数的广义势。进行了详细的计算以揭示引入的技术。同样，基于位于拉伸和压缩子午线上的典型测试，论证了这种电势的校准方法，该方法可产生明确的数学公式。对于上述取决于劳德角的耗散函数，它们的范围缩小了（由Ottosen提出）。最后，给出了三个涉及经典势的示例：Beltrami势，Drucker-Prager势和Mises-Schleicher势函数使用形状函数的广义势。进行了详细的计算以揭示引入的技术。同样，基于位于拉伸和压缩子午线上的典型测试，论证了这种电势的校准方法，该方法可产生明确的数学公式。对于上述取决于劳德角的耗散函数，它们的范围缩小了（由Ottosen提出）。最后，给出了三个涉及经典势的示例：Beltrami势，Drucker-Prager势和Mises-Schleicher势函数使用形状函数的广义势。进行了详细的计算以揭示引入的技术。同样，基于位于拉伸和压缩子午线上的典型测试，论证了这种电势的校准方法，该方法可产生明确的数学公式。进行了详细的计算以揭示引入的技术。同样，基于位于拉伸和压缩子午线上的典型测试，论证了这种电势的校准方法，该方法可产生明确的数学公式。进行了详细的计算以揭示引入的技术。同样，基于位于拉伸和压缩子午线上的典型测试，论证了这种电势的校准方法，该方法可产生明确的数学公式。