AI 中文总结
研究针对参数化非线性固体力学模拟成本高的问题，提出PI-GINOT这一无数据几何信息神经算子，通过特定方法预测狗骨形试件有限应变超弹性响应，经训练和验证，在多个测试几何形状上取得一定精度结果，揭示了局部应力分辨率待提升之处。
AI 中文摘要
参数化非线性固体力学模拟广泛应用于虚拟测试、优化和不确定性分析，但当几何形状改变时，重复的有限元模拟成本高昂。本文提出了PI-GINOT，一种物理信息神经算子，可在不使用有限元训练数据的情况下预测四参数狗骨形试件家族的有限应变超弹性响应。每个试件由边界点云描述并编码为几何特征，通过交叉注意力解码器预测任意点的位移，精确施加位移边界条件，利用自动微分和可压缩Neo-Hookean平面应力模型计算应力。训练由平衡、无牵引力和对称条件、变形稳定性和内力一致性指导。仅在训练后使用Abaqus模拟进行验证。在八个测试几何形状上，PI-GINOT实现了2.1%-7.1%的位移误差、0.9%-13.3%的峰值冯·米塞斯应力误差和低于10.3%的截面力误差。单个应力分量中出现较大误差，特别是对于窄试件，主要是因为在标距到圆角过渡处应力梯度陡峭。这些结果表明，PI-GINOT可以在没有标记模拟数据的情况下为非线性固体力学提供有用的几何相关预测，同时也揭示了仍需要更好的局部应力分辨率的地方。
英文摘要
Parametric nonlinear solid-mechanics simulations are widely used in virtual testing, optimisation, and uncertainty analysis, but repeated finite-element simulations become costly when geometry changes. This paper presents PI-GINOT, a physics-informed neural operator that predicts finite-strain hyperelastic responses across a four-parameter family of DogBone specimens without using finite-element training data. Each specimen is described by a boundary point cloud, which is encoded into geometry features. A cross-attention decoder then predicts displacement at arbitrary points. Displacement boundary conditions are enforced exactly, while stresses are computed using automatic differentiation and a compressible Neo-Hookean plane-stress model. Training is guided by equilibrium, traction-free and symmetry conditions, deformation stability, and internal force consistency. Abaqus simulations are used only after training for validation. Across eight test geometries, PI-GINOT achieves displacement errors of 2.1%-7.1%, peak von Mises stress errors of 0.9%-13.3%, and section-force errors below 10.3%. Larger errors occur in individual stress components, especially for narrow specimens, mainly because of steep stress gradients near the gauge-to-fillet transition. These results show that PI-GINOT can provide useful geometry-dependent predictions for nonlinear solid mechanics without labelled simulation data, while also revealing where better local stress resolution is still needed.
