This paper introduces a new local plastic correction algorithm developed to accelerate finite element simulations for structures with elasto-plastic constitutive laws. The proposed method belongs to the category of generalized multiaxial Neuber-type methods enabled by pointwise proportional evolution rules. The algorithm numerically integrates J2 plasticity laws as a function of the finite element elastic response of the structure, to obtain full-field 3D elasto-plastic quantities for any proportionally applied loading. Examples of the numerical capabilities of this algorithm are shown on a structure containing a distribution of pores, for monotonic and fatigue loading. The approximation errors due to the proposed local plastic correction are also investigated. As a second point of innovation, we show that the proposed local plastic correction can be accelerated when dealing with large-scale structures by employing a simple meta-model, with virtually no added errors. Finally, we develop and investigate the merits of an additional deep-learning-based corrective layer to reduce approximations errors on a subset of structures for which full elasto-plastic FE simulations are performed, the solutions of which are subsequently used as training set for a Convolutional Neural Network algorithm designed to learn the error between full FE and plastic correction approximations.

翻译：本文提出一种新型局部塑性修正算法，旨在加速含弹塑性本构关系的结构有限元模拟。该算法属于基于逐点比例演化律的广义多轴Neuber型方法范畴。通过数值积分J2塑性定律（作为结构有限元弹性响应的函数），可对任意比例加载工况获取全场三维弹塑参量。本文以含孔隙分布的结构为例，展示了该算法在单调加载与疲劳加载场景下的数值能力，并探究了所提局部塑性修正带来的近似误差。作为第二创新点，我们证明当处理大规模结构时，通过采用简单元模型可在几乎不引入额外误差的情况下加速局部塑性修正。最后，我们开发并验证了基于深度学习的附加修正层，该层可缩减子结构（对其实施完整弹塑性有限元模拟）的近似误差；其求解结果随后用作卷积神经网络算法的训练集，该网络旨在学习全有限元解与塑性修正近似值之间的误差。