Thanks to advances of techniques like digital image correlation (DIC), the virtual fields method (VFM) has become a common approach to identifying mechanical parameters of materials when full-field displacement data are available. However, it is limited to a priori selected classical material models. Recently, machine learning and model discovery has become a promising alternative for non-parametric material identification. This paper proposes an approach using a machine learning framework (NN-EUCLID) combined with the VFM. This framework has already demonstrated its good performance for hyperelasticity using 2D simulated displacement fields and a loss function formulated with the local equilibrium gap. Our study focuses on training a similar NN-EUCLID framework with 3D displacement fields obtained in a bulge inflation test to discover mechanical models of arteries. Instead of using the local equilibrium gap, we employ the VFM to formulate loss functions. This novelty allows us to address issues such as unknown boundary conditions. We present numerical examples showcasing the ability to train hyperelastic models for isotropic and anisotropic materials. Results obtained with experimental data demonstrate the method’s effectiveness in training neural-network constitutive models for biological tissues using accessible full-field measurements.

中文翻译：

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基于机器学习的虚场方法：各向异性超弹性的应用


由于数字图像相关 （DIC） 等技术的进步，当全场位移数据可用时，虚场法 （VFM） 已成为识别材料力学参数的常用方法。但是，它仅限于先验选择的经典材料模型。最近，机器学习和模型发现已成为非参数材料识别的有前途的替代方案。本文提出了一种使用机器学习框架 （NN-EUCLID） 结合 VFM 的方法。该框架已经使用 2D 模拟位移场和用局部平衡间隙公式化的损失函数证明了其在超弹性方面的良好性能。我们的研究重点是使用在凸起充气测试中获得的 3D 位移场来训练类似的 NN-EUCLID 框架，以发现动脉的机械模型。我们没有使用局部均衡间隙，而是使用 VFM 来构建损失函数。这种新颖性使我们能够解决未知边界条件等问题。我们提供了数值示例，展示了为各向同性和各向异性材料训练超弹性模型的能力。通过实验数据获得的结果表明，该方法在使用可访问的全场测量来训练生物组织的神经网络本构模型方面的有效性。