标题： 基于变分匹配灵敏度的虚拟场用于超弹性材料模型标定 显示英文标题

标题： Variation-matching sensitivity-based virtual fields for hyperelastic material model calibration

摘要： 从三维全场变形数据中准确识别非线性材料参数仍然是实验力学中的一个挑战。虚拟场方法（VFM）为材料模型校准提供了一种强大且计算高效的途径，然而，其成功在很大程度上取决于虚拟场的选择以及可用运动学数据的信息量。在本工作中，我们通过在一个基于应变不变量的建模框架内系统地开发和比较替代的变分和解析SBVF，推进了基于敏感性的虚拟场（SBVF）方法的最新离散公式。本工作的核心贡献是实现了基于变分的SBVFs（vSBVFs），这些SBVFs使用方向Gâteaux导数进行公式化，以及从解析微分得到的虚拟场（aSBVFs），这些虚拟位移场提供了针对特定模型的显式虚拟位移场用于参数识别。利用模拟的噪声体积数据集，我们证明vSBVFs和aSBVFs能够实现每个材料参数的程序化、自动化最优虚拟场构建，显著提高了校准的鲁棒性和效率，而无需手动选择场或在数据采集中需要高时间分辨率。我们量化了数据丰富度——采样运动学状态的有效多样性——表明通过样本几何和加载协议增加数据丰富度可以提高参数可识别性。这些发现建立了一条适用于未来与软性复杂材料的实验全场成像部署的自动、抗噪声的材料模型校准路径，并为优化形状拓扑以及扩展到粘弹性及各向异性行为提供了基础。 显示英文摘要

摘要： Accurate identification of nonlinear material parameters from three-dimensional full-field deformation data remains a challenge in experimental mechanics. The virtual fields method (VFM) provides a powerful, computationally efficient approach for material model calibration, however, its success depends critically on the choice of virtual fields and the informativeness of available kinematic data. In this work, we advance the state-of-the-art discrete formulation of the sensitivity-based virtual fields (SBVF) method by systematically developing and comparing alternative variational and analytical SBVFs within a strain-invariant-based modeling framework. A central contribution of this work is the implementation and assessment of variation-based SBVFs (vSBVFs), formulated using directional G\^ateaux derivatives, as well as virtual fields derived from analytical differentiation (aSBVFs) which provide explicit, model-tailored virtual displacement fields for parameter identification. Using simulated noisy volumetric datasets, we demonstrate that vSBVFs and aSBVFs enable procedural, automated construction of optimal virtual fields for each material parameter, substantially enhancing the robustness and efficiency of calibration without the need for manual field selection or high temporal resolution in the data acquisition. We quantify data richness -- the effective diversity of sampled kinematic states -- showing that increased data richness via sample geometry and loading protocols leads to improved parameter identifiability. These findings establish a pathway for automated, noise-robust material model calibration suitable for future deployment with experimental full-field imaging of soft, complex materials, and provide a foundation for optimizing shape topology and extending to viscoelastic and anisotropic behaviors.