In this paper, we present a finite elasto-plasticity theory for large plastic deformations. For the elastic part of the model, we use the St. Venant–Kirchhoff elasticity. The plastic part is described by the isomorphy concept, the yield condition is covered by the isotropic \(J_2\) theory of (Huber in Czas Techn 22:34,1904; von Mises in Math Phys 4:582–592, 1913) and (Hencky in ZAMM 9:215–220, 1924), and the yield condition uses the principle of maximum plastic dissipation. The numeric of this theory is discussed and finally implemented in a Fortran code to use it as material law in the UMAT subroutine of the finite element program Abaqus. The material law is validated using different test calculations like tensile and shear tests as well as a large deformation simulation compared to the Abaqus internal material law. Further, we apply this material model to determine the effective material stiffness tetrad of large deformed inhomogeneous materials. For these purposes, we additionally present an automated method for determining material stiffnesses of an arbitrary material in Abaqus.

在本文中，我们提出了大塑性变形的有限弹塑性理论。对于模型的弹性部分，我们使用圣维南-基尔霍夫弹性。塑性零件由同构概念描述，屈服条件由各向同性\(J_2\)理论覆盖(Huber in Czas Techn 22:34,1904; von Mises in Math Phys 4:582–592, 1913)， （Hencky in ZAMM 9:215–220, 1924），屈服条件使用最大塑性耗散原理。该理论的数值被讨论并最终在 Fortran 代码中实现，以将其用作有限元程序 Abaqus 的 UMAT 子程序中的材料定律。与 Abaqus 内部材料定律相比，使用拉伸和剪切测试等不同的测试计算以及大变形模拟来验证材料定律。此外，我们应用该材料模型来确定大变形非均匀材料的有效材料刚度四分体。为此，我们还提出了一种在 Abaqus 中确定任意材料的材料刚度的自动化方法。