This work presents a Finite Element Model Updating inverse methodology for reconstructing heterogeneous material distributions based on an efficient isogeometric shell formulation. It uses a nonlinear material model with a hyperelastic incompressible Neo-Hookean membrane part and a Canham bending part. The material distribution is discretized by linear elements such that the nodal values are the design variables to be identified. Independent FE and material discretization, as well as flexible incorporation of experimental data, offer high robustness and control. Three elementary test cases, which exhibit large deformations and different challenges, are considered: uniaxial tension, pure bending, and sheet inflation. Experiment-like results are generated from high-resolution simulations with the subsequent addition of up to 4% noise. Local optimization based on the trust-region approach is used. The results show that with a sufficient amount of experimental measurements, the algorithm is capable to reconstruct material distributions with high precision even in the presence of large noise. The proposed formulation is very general, facilitating its extension to other material models and optimization algorithms. For the latter, the analytically derived sensitivities are provided.

中文翻译：

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异质等几何 Kirchhoff-Love 壳的非线性材料识别

这项工作提出了一种有限元模型更新逆方法，用于基于有效的等几何壳公式重建异质材料分布。它使用具有超弹性不可压缩 Neo-Hookean 膜部件和 Canham 弯曲部件的非线性材料模型。材料分布由线性元素离散化，因此节点值是要识别的设计变量。独立的有限元和材料离散化，以及实验数据的灵活结合，提供了高度的鲁棒性和控制。考虑了表现出大变形和不同挑战的三个基本测试案例：单轴拉伸、纯弯曲和板材膨胀。类似实验的结果是从高分辨率模拟中产生的，随后添加了高达 4% 的噪声。使用基于信任区域方法的局部优化。结果表明，通过足够数量的实验测量，即使在存在大噪声的情况下，该算法也能够高精度地重建材料分布。所提出的公式非常通用，有助于将其扩展到其他材料模型和优化算法。对于后者，提供了分析得出的灵敏度。