用神经网络替代传统材料模型，直接嵌入有限元软件实现高精度模拟。
Embedding an ANN-Based Crystal Plasticity Model into the Finite Element Framework using an ABAQUS User-Material Subroutine
- 将训练好的神经网络作为本构关系，通过用户材料子程序接入有限元框架。
- 可直接从应变历史预测应力并计算雅可比矩阵，支持复杂非线性行为模拟。
- 适合需要高精度材料响应的仿真场景，尤其适用于多尺度力学建模。
本文提出一种将训练好的神经网络（NN）嵌入有限元（FE）框架的实用方法，通过 ABAQUS 用户材料子程序（UMAT）实现。该方法以晶体塑性为例，处理复杂的非线性、路径依赖材料响应，具有广泛的应用前景。利用 UMAT 子程序可直接根据应变历史预测应力及其他力学性能，并通过反向传播或数值微分计算雅可比矩阵，对求解收敛至关重要。该方法使训练好的机器学习模型作为数据驱动的本构关系在有限元中使用，保留了传统本构模型常忽略或平均化的多尺度信息。该方法具有高度灵活性，适用于其他材料行为和有限元工具。尽管预期能更准确再现真实材料行为，但需特别关注求解可靠性与收敛条件。相关理论见 Heider 等人 (2020)，示例代码已公开提供。
原文摘要 · Abstract (English)
This manuscript presents a practical method for incorporating trained Neural Networks (NNs) into the Finite Element (FE) framework using a user material (UMAT) subroutine. The work exemplifies crystal plasticity, a complex inelastic non-linear path-dependent material response, with a wide range of applications in ABAQUS UMAT. However, this approach can be extended to other material behaviors and FE tools. The use of a UMAT subroutine serves two main purposes: (1) it predicts and updates the stress or other mechanical properties of interest directly from the strain history; (2) it computes the Jacobian matrix either through backpropagation or numerical differentiation, which plays an essential role in the solution convergence. By implementing NNs in a UMAT subroutine, a trained machine learning model can be employed as a data-driven constitutive law within the FEM framework, preserving multiscale information that conventional constitutive laws often neglect or average. The versatility of this method makes it a powerful tool for integrating machine learning into mechanical simulation. While this approach is expected to provide higher accuracy in reproducing realistic material behavior, the reliability of the solution process and the convergence conditions must be paid special attention. While the theory of the model is explained in [Heider et al. 2020], exemplary source code is also made available for interested readers [https://doi.org/10.25835/6n5uu50y]
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