AI 中文总结
本文针对并发多尺度模拟中的塑性回映过程，介绍用简单前馈网络构建轻量级神经网络替代模型的方法，阐述工作流程、进行敏感性研究，该模型能大幅降低分析成本，且方法可扩展到三维及其他情况。
AI 中文摘要
本文为在并发多尺度（FE2）模拟中的塑性回映过程构建轻量级神经网络替代模型提供实用指南。并非提出新架构，而是展示一个精心设计的简单前馈网络，通过模仿经典回映更新，可取代传统基于中尺度FFT均匀化的FE2方案中成本高昂的嵌套细尺度求解。详细介绍完整工作流程，包括从增量均匀化分析生成训练数据、构建紧凑且充分的数据集、将材料对称性直接嵌入映射以及在标准有限元求解器中作为用户定义材料子程序部署训练好的网络。通过敏感性研究考察模型对数据密度、增量大小和网格细化的鲁棒性。对于宏观各向同性的二维平面应力情况，替代模型能再现参考响应，将每次分析成本从数小时降至数秒，加速比高达30000倍。该方法在适当采样策略和数据集下可自然扩展到三维及较弱对称性假设情况。
英文摘要
This paper presents a practical guide to building lightweight neural-network surrogates for the plastic return-mapping process in concurrent multiscale (FE2) simulations. Rather than proposing a new architecture, we show how a deliberately simple feed-forward network, structured to mirror the classical return-mapping update, can replace the prohibitively expensive nested fine-scale solves that dominate the cost of conventional FE2 schemes based on FFT homogenization at the meso-scale. We walk through the full workflow: generating training data from incremental homogenization analyses, constructing a compact yet sufficient dataset, embedding material symmetries directly into the mapping, and deploying the trained network as a user-defined material subroutine (UMAT) in a standard finite-element solver -- enabling widespread use. A sensitivity study examines the model's robustness to data density, increment size, and mesh refinement, and we characterize the regimes in which the surrogate holds and where it breaks down. For the macroscopically isotropic, two-dimensional plane-stress setting considered here, the surrogate reproduces the reference response while reducing the per-analysis cost from hours to seconds with speed-ups up to 30,000 over standard FE2. The approach extends naturally to three dimensions and to weaker symmetry assumptions, given an appropriate sampling strategy and dataset.
