基于全场数据的神经超弹性模型可靠训练

中文摘要 AI 辅助

我们系统研究了基于平衡间隙的超弹性物理增强神经网络（PANNs）校准的鲁棒性和局限性，其中我们考虑了各向同性和多凸PANNs的特殊情况。在全场参数化中，通常假设位移场以足够的空间分辨率被捕获，以便准确评估变形场，并且假设试样足够薄，使得平面应力近似成立。由于这些假设在真实实验中从未理想满足，我们使用合成生成的数据，研究了欠分辨的表面测量和不可忽略的试样厚度如何严重影响模型参数化。此外，我们对一组非均匀试样几何形状的真实实验数据进行了校准。我们表明，校准期间可接受的变形状态的覆盖范围决定了模型泛化到未见几何形状和载荷情况的能力；这种能力可以通过适当的试样组合进一步提高。然而，准确描绘这一丰富数据背后的材料行为需要足够灵活的本构模型，而PANNs非常适合这一点。然而，仅靠丰富的变形状态覆盖是不够的：除非校准数据包含双轴拉伸类状态，否则包含第二变形不变量的模型会向等双轴拉伸方向进行非物理外推，而将PANN限制为第一不变量则保持可靠。

英文摘要

We present a systematic investigation of the robustness and limitations of equilibrium gap-based calibrations for hyperelastic physics-augmented neural networks (PANNs), where we consider the special case of isotropic and polyconvex PANNs. In full-field parameterizations, it is commonly assumed that the displacement field is captured with sufficient spatial resolution for an accurate evaluation of the deformation field, and that the specimen is thin enough for plane stress to hold to a good approximation. Since these assumptions are never ideally satisfied in real experiments, we investigate, using synthetically generated data, how severely an under-resolved surface measurement and a non-negligible specimen thickness can affect the model parameterization. Furthermore, we perform calibration on real experimental data for a set of inhomogeneous specimen geometries. We show that the coverage of the admissible deformation states during calibration governs the ability of a model to generalize to unseen geometries and load cases; this ability can be improved further by appropriate combinations of specimens. Accurately depicting the material behavior underlying this rich data, however, requires a sufficiently flexible constitutive model, for which PANNs are well suited. Yet a rich coverage of deformation states alone is not sufficient: unless the calibration data comprise biaxial-tension-like states, models that include the second deformation invariant extrapolate unphysically towards equi-biaxial tension, whereas restricting the PANN to the first invariant remains reliable.

发表机构

• Institute of Solid Mechanics, TU Dresden（德累斯顿工业大学固体力学研究所）
• DCMS – Dresden Center for Computational Materials Science（德累斯顿计算材料科学中心）

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