arXiv:2606.19375cs.LGcond-mat.mtrl-sci2026-06

用神经网络从位移和力数据中自动发现材料屈服准则,无需应力或塑性应变数据。

Physics-Informed Discovery of Yield Functions in Plasticity via Convex Neural Representations

论文配图:Physics-Informed Discovery of Yield Functions in Plasticity via Convex Neural Representations
图 1 · 摘自论文原文
  • 用凸神经网络建模屈服函数,强制满足力学约束条件。
  • 在多个加载工况下通过力平衡损失训练,实现无监督学习。
  • 适用于缺乏直接应力观测的工程场景,适合材料本构建模研究者。

识别各向异性屈服函数仍具挑战性,因为屈服现象无法在全场力学测量中直接观测,方向校准需大量加载方向,且合适解析形式的选择非易事。本文提出一种物理信息框架,仅基于全场位移数据与反力数据,无需应力观测、塑性应变测量、直接屈服面数据或预设参数化屈服函数,即可发现屈服函数。该框架将屈服函数视为弹塑性应力积分中的力学约束本构组件,而非依赖应力空间监督。屈服函数由一个凸神经网络表示,强制满足凸性、一次齐次性及张力-压缩对称性,并通过可微应力更新与多工况下的物理信息力平衡损失进行训练。框架在包含冯·米塞斯、Hill 1948 和 Yld2000-2d 屈服函数的有限元基准测试中验证,评估了屈服轮廓吻合度、位移噪声敏感性、通过塑性活跃应力状态的可辨识性、认知不确定性及多项式代理模型部署效果。本研究为从位移与力数据中发现各向异性屈服函数提供了一条力学约束路径,同时确保所识别成分保持弹塑性应力积分结构。

原文摘要 · Abstract (English)

Identifying anisotropic yield functions remains challenging since yielding is not directly observed in full-field mechanical measurements, directional calibration can require many loading directions, and selecting an appropriate analytical form is nontrivial. This study proposes a physics-informed framework for discovering yield functions from full-field displacement data and reaction force data, without stress observations, plastic strain measurements, direct yield surface data, or a prescribed parametric yield function. The framework identifies the yield function as a mechanically constrained constitutive component inside elastoplastic stress integration, rather than through direct stress-space supervision. The yield function is represented by a convex neural network that enforces convexity and positive homogeneity of degree one while imposing the assumed tension-compression symmetry, and this neural yield function is trained with a differentiable stress update and a physics-informed force equilibrium loss across multiple loading cases. The proposed framework is validated using finite element (FE) benchmark studies with von Mises, Hill 1948, and Yld2000-2d yield functions, assessing yield contour agreement, displacement-noise sensitivity, identifiability through plastically active stress states, epistemic uncertainty, and polynomial-surrogate deployment. This study provides a mechanics-constrained pathway for discovering anisotropic yield functions from displacement and force data while keeping the identified component within the structure of elastoplastic stress integration.

屈服函数神经网络物理信息材料建模

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