Finite element simulations of structures with nonlinear material behavior require advanced material models to provide accurate predictions. However, the computational costs of these models can be high, as they solve coupled differential algebraic equations at each integration point, in each equilibrium iteration, in every time step. In this study, we propose a machine learning-based framework to accelerate these computations by explicitly calculating the state variable updates with neural networks, enabling large time steps with low computational costs. The neural networks operate on invariants, and the necessary and sufficient evolution directions are determined analytically based on the training data. Furthermore, the proposed framework enforces exact fulfillment of the plastic consistency condition. To evaluate the proposed framework, a prototype model with the von Mises yield criterion and nonlinear kinematic hardening is chosen. Only 10 cycles of multiaxial proportional loading are used to generate the training data. After evaluating the proposed framework in material point simulations, we incorporate it into finite element simulations to evaluate its accuracy and computational efficiency in a boundary value problem. The results from both material point and finite element simulations show a very promising numerical performance of the neural network-based time integrator. It provides very good accuracy and numerical stability, as well as a noticeable gain in computational time for a single strain increment per load segment.

翻译：有限元模拟中，具有非线性材料行为的结构需要先进材料模型来提供精确预测。然而，这些模型的计算成本可能很高，因为它们需要在每个时间步的每次平衡迭代中，于每个积分点求解耦合的微分代数方程。在本研究中，我们提出了一种基于机器学习的框架来加速这些计算，通过神经网络显式计算状态变量更新，从而实现大时间步长和低计算成本。神经网络以不变量为输入，并基于训练数据解析地确定必要且充分的演化方向。此外，所提出的框架强制精确满足塑性一致性条件。为了评估该框架，我们选取了具有冯·米塞斯屈服准则和非线性运动硬化的原型模型，仅使用10个多轴比例加载循环生成训练数据。在材料点模拟中评估该框架后，我们将其纳入有限元模拟，以评估其在边值问题中的精度和计算效率。材料点和有限元模拟的结果均表明，基于神经网络的时间积分器具有非常出色的数值性能，它提供了良好的精度和数值稳定性，并且在每个载荷段仅需一次应变增量时，显著节省了计算时间。