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Lightweight return-mapping surrogates for multiscale plasticity: a practical guide
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DOI：10.1007/s00466-026-02849-9.png)
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Abstract
En 中文
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. Moreover, by eliminating the need to store and update the extensive microscale state variables, it drastically reduces memory requirements and enables substantially finer finite element discretizations that would otherwise be impossible. The approach extends naturally to three dimensions and to weaker symmetry assumptions, given an appropriate sampling strategy and dataset.
Keywords:
Deep learning
Neural network surrogate
Data-driven plasticity
Plastic return-mapping
Concurrent multiscale simulation
FFT-based homogenization
Journal
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3.8
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3.2K
Citations:
9.0K
