提出新型材料本构模型,训练快且对加载路径分辨率不敏感。
Constitutive State-Space Modeling of Path-Dependent Plasticity: A Resolution-Consistent and Parallelizable Computational Framework

- 用状态空间建模重构增量本构关系,实现并行训练。
- 在粗略路径离散下误差仍低,验证损失降低一个数量级。
- 适合长历史数据的高效建模,尤其适合物理规律明确的材料。
基于数据驱动的路径相关塑性本构模型通常采用非线性循环神经网络,其序列状态演化限制了并行训练,且预测结果可能依赖于应变路径的离散化。本文提出一种结构化状态空间(CSS)模型,将受力学启发的状态空间动力学重构为增量本构算子。应变增量分解为幅值与方向:加载方向驱动隐状态系统,幅值则通过零阶保持方式离散化连续时间线性递推。该设计确保零增量下的平稳性,显著降低对路径离散化的敏感度,并保留S5模型的并行扫描结构,实现长历史数据的高效训练。在包括各向同性J2塑性、压力敏感泡沫塑性及混合各向同性-运动硬化在内的四种多轴路径相关材料模型中,CSS在预测精度上达到或超过最小状态单元(MSC)架构,尤其在不可压缩塑性材料上验证损失降低一个数量级。更重要的是,当评估路径离散化比训练时更粗时,CSS误差保持稳定,而MSC误差大幅上升。CSS训练速度更快,所需应力-应变样本更少即可达到相当或更优性能。对学习到的状态分析显示,其隐结构与底层物理本构模型的维度一致。结果证明,基于力学设计的结构化状态空间动力学是高效且离散化鲁棒的数据驱动本构建模框架。
原文摘要 · Abstract (English)
Data-driven constitutive models for path-dependent plasticity are commonly formulated using nonlinear recurrent neural networks, whose sequential state evolution limits parallel training and whose predictions may depend on the discretization of the applied strain path. We introduce a Constitutive State Space (CSS) model that reformulates structured state-space dynamics as an incremental constitutive operator. The strain increment is decomposed into magnitude and direction: the loading direction drives the latent state-space system, while the increment magnitude enters the zero-order-hold discretization of its continuous-time linear recurrence. This mechanics-tailored construction guarantees stationarity under zero increments, strongly reduces sensitivity to strain-path resolution, and retains the parallel-scan structure of S5 for efficient training on long constitutive histories. The CSS and Minimal State Cell (MSC) architectures are compared for four multiaxial path-dependent material models including isotropic J2 plasticity, pressure-sensitive foam plasticity, and combined isotropic-kinematic hardening. CSS matches or exceeds the prediction accuracy of the MSC, including one order of magnitude lower validation losses for the plastically incompressible materials. Importantly, CSS maintains low errors across large changes in strain-path discretization, whereas the MSC error increases substantially when evaluated at coarser resolutions than used for training. CSS trains substantially faster and requires fewer strain-stress pairs to attain comparable or better accuracy. Analysis of the learned state further reveals latent structure consistent with the dimensionality of the underlying physical constitutive models. These results establish mechanics-tailored structured state-space dynamics as a computational framework for efficient and discretization-robust data-driven constitutive modeling.
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