arXiv:2609.02194cs.LGcs.CE2026-09

用神经算子和因果注意力建模材料本构,仅凭应力应变数据就能预测塑性与损伤行为。

Learning the Constitutive Behavior of Materials via Neural Operators and Causal Attention: Case Studies in Plasticity and Damage

论文配图:Learning the Constitutive Behavior of Materials via Neural Operators and Causal Attention: Case Studies in Plasticity and Damage
图 1 · 摘自论文原文
  • 将材料视为从应变历史到应力响应的函数映射,直接学习完整加载路径。
  • 在多维非线性塑性和延性损伤模型上实现高精度预测,且计算可并行化。
  • 适合材料建模、力学仿真等需要高效精准本构关系的工程场景。

传统弹塑性材料的本构建模依赖于需人工假设的内部状态变量及其演化方程,但实际中许多内部变量不可测,只能从测量的应力-应变数据中推断本构关系。本文提出一种基于材料算子的数据驱动建模框架,将变形材料视为从完整应变历史到对应应力响应的函数映射。与传统自回归或递归模型不同,该模型直接以全加载路径作为函数到函数的映射进行训练,通过单次并行前向传播预测完整的应力轨迹。时间路径依赖性通过嵌入算子中的因果掩码注意力机制实现,仅允许模型关注过去材料状态,同时保持计算并行性。频域中的谱卷积提供离散化不变表示,而因果注意力捕捉高度自适应的非局部历史依赖。此外,正弦激活函数用于解析弹塑性区域中的强非线性跃迁。框架在多维、速率无关的材料模型(重点为非线性塑性和延性损伤累积)上评估,结果表明其能准确稳健地预测不可逆变形机制,同时具备分辨率不变性和优异的并行效率。

原文摘要 · Abstract (English)

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.

材料建模神经算子因果注意力非线性力学

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