Abstract With the goal of improving upon the accuracy of D. Arnold's MINI element for finite strain plasticity, and more precisely calculate the elastic/plastic interface, we extend this element formulation to include, as nodal degrees-of-freedom, a function of the second invariant of the deviatoric stress, J2. A finite-strain J2 − u − p mixed formulation of the classical low-order tetrahedron element is introduced. We therefore have continuous displacements, pressures and J2. This element contains an internal displacement bubble that is not condensed out. For hyperelastic materials, we adopt a relative Green-Lagrange formulation whose conjugate stress approximates the Cauchy stress. For the elasto-plastic case, we combine this formulation with the elastic Mandel stress construction, which is power-consistent with the plastic strain rate. In contrast with nodally integrated and variational multiscale methods, there are no additional parameters. High accuracy is obtained for four-node tetrahedra with three incompressibility and bending benchmarks being solved. Accuracy similar to the F ¯ hexahedron are obtained. Although the ad-hoc factor is removed and performance is competitive, computational cost is higher than MINI's, with each tetrahedron containing 23 degrees-of-freedom.

中文翻译：

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有限应变混合 J2 − u − p 低阶四面体

摘要 为了提高 D. Arnold 的 MINI 有限应变塑性单元的精度，并更精确地计算弹塑性界面，我们扩展了该单元公式，以包括作为节点自由度的函数偏应力的第二个不变量，J2。引入了经典低阶四面体单元的有限应变 J2 − u − p 混合公式。因此，我们有连续的位移、压力和 J2。该元素包含一个未冷凝的内部位移气泡。对于超弹性材料，我们采用相对的 Green-Lagrange 公式，其共轭应力近似于柯西应力。对于弹塑性外壳，我们将此公式与弹性曼德尔应力结构相结合，该结构与塑性应变率功率一致。与节点积分和变分多尺度方法相比，没有额外的参数。求解三个不可压缩性和弯曲基准的四节点四面体获得了高精度。获得了类似于 F¯六面体的精度。尽管去除了临时因素并且性能具有竞争力，但计算成本高于 MINI，每个四面体包含 23 个自由度。