基于神经算子与因果注意力学习材料的本构行为：在塑性与损伤中的案例研究
Learning the Constitutive Behavior of Materials via Neural Operators and Causal Attention: Case Studies in Plasticity and Damage
- Institute of Applied Mechanics, RWTH Aachen University（亚琛工业大学应用力学研究所）
- ACCESS e.V.（ACCESS协会）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究提出结合神经算子与因果注意力的材料本构建模框架，可从应变-应力数据准确预测材料不可逆变形，兼具分辨率不变性与并行效率，在塑性和损伤案例中表现优异。
AI中文摘要：
路径依赖非弹性材料的经典本构建模依赖于内部状态变量，其演化方程必须基于领域知识假设，并通过实验数据校准。然而，在许多实际场景中，相关内部变量通常无法在实验中测量，必须完全从测得的应变-应力数据中推断本构响应，且无需任何关于材料内部状态的先验知识。我们提出一种基于材料算子概念的数据驱动本构建模框架，该框架将变形材料视为从其整个应变历史到对应应力响应的函数映射。与传统自回归或循环公式不同，该模型直接在完整加载路径上训练，作为函数到函数的映射，在单次并行前向传播中预测完整应力轨迹。时间路径依赖性通过嵌入算子内的因果掩码注意力机制实现，该机制将模型的注意力限制在过去的材料状态，同时保留计算并行性。谱卷积在频域提供与分辨率无关的表示，而因果注意力捕捉高度自适应的非局部历史依赖性。此外，使用正弦激活函数解决非弹性状态下固有的强非线性转变。该框架在表现出复杂现象的多维、率无关材料模型上进行评估，重点关注非线性塑性与延性损伤累积。结果表明，该模型对不可逆变形机制的预测准确且鲁棒，同时实现了分辨率不变性和出色的并行效率。
英文摘要：
Classical constitutive modeling of path-dependent inelastic materials relies on internal state variables whose evolution equations must be postulated based on domain knowledge and calibrated against experimental data. However, in many practical settings, the relevant internal variables are typically not measurable in experiments, and the constitutive response must be inferred entirely from measured strain-stress data without any prior knowledge of the material's internal state. We propose a data-driven constitutive modeling framework based on the concept of a material operator, which treats a deforming material as a functional mapping from its entire strain history to the corresponding stress response. In contrast to traditional autoregressive or recurrent formulations, the model is trained directly on full loading paths as function-to-function mappings, predicting complete stress trajectories in a single parallel forward pass. Temporal path dependence is enforced through a causally masked attention mechanism embedded within the operator, which restricts the model's attention to past material states while preserving computational parallelizability. Spectral convolutions provide discretization-invariant representations in the frequency domain, while causal attention captures highly adaptive, non-local history dependence. Furthermore, sinusoidal activation functions are used to resolve the strong nonlinear transitions inherent in inelastic regimes. The framework is evaluated across multidimensional, rate-independent material models exhibiting complex phenomena, with an emphasis on nonlinear plasticity and ductile damage accumulation. The results demonstrate accurate and robust predictions of irreversible deformation mechanisms while simultaneously achieving resolution invariance and excellent parallel efficiency.
