发表机构
ETH Zurich; inspire AG; Brown University（苏黎世联邦理工学院; inspire AG; 布朗大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对路径依赖塑性，提出本构状态空间（CSS）模型，将结构化状态空间动力学重构为增量本构算子，实现并行训练、分辨率鲁棒且高效的数据驱动本构建模，在多种材料模型上精度优于或媲美MSC，并显著降低训练成本。
AI 中文摘要
路径依赖塑性的数据驱动本构模型通常使用非线性递归神经网络构建，其顺序状态演化限制了并行训练，且其预测可能依赖于所施加应变路径的离散化。我们提出了一种本构状态空间（CSS）模型，将结构化状态空间动力学重新表述为增量本构算子。应变增量被分解为大小和方向：加载方向驱动潜在的状态空间系统，而增量大小则进入其连续时间线性递推的零阶保持离散化。这种针对力学定制的构造保证了零增量下的平稳性，显著降低了对应变路径分辨率的敏感性，并保留了S5的并行扫描结构，以便在长本构历史上进行高效训练。将CSS和最小状态单元（MSC）架构在四种多轴路径依赖材料模型上进行了比较，包括各向同性J2塑性、压力敏感泡沫塑性和组合各向同性-随动硬化。CSS匹配或超过了MSC的预测精度，包括对于塑性不可压缩材料，验证损失低一个数量级。重要的是，CSS在应变路径离散化的大变化下保持低误差，而MSC在比训练时更粗的分辨率下评估时误差显著增加。CSS训练速度明显更快，并且需要更少的应变-应力对即可达到相当或更好的精度。对学习到的状态的分析进一步揭示了与底层物理本构模型维度一致的潜在结构。这些结果确立了针对力学定制的结构化状态空间动力学作为高效且对离散化鲁棒的数据驱动本构建模的计算框架。
英文摘要
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.
