基于接触的空间非均质固体非线性材料识别的逆分析
Contact-based inverse analysis for nonlinear material identification in spatially heterogeneous solids
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中文总结 AI 辅助
研究提出基于接触的等几何有限元模型更新框架识别非线性固体空间变化本构参数，利用全场位移测量等，通过低阶拉格朗日插值离散，用信赖域反射算法优化，经数值示例验证方法可行性与有效性，还能提升计算效率。
中文摘要 AI 辅助
本研究提出了一种基于接触的等几何有限元模型更新（FEMU）框架，用于识别非线性固体的空间变化本构参数。该公式考虑了由于机械接触导致的超弹性三维固体和薄壳的大准静态变形。所提出的逆方法利用至少在自由表面上可用的全场位移测量，以及在纯狄利克雷边界条件下的合力。非均匀材料参数场使用与等几何分析网格无关的低阶拉格朗日插值进行离散化，从而控制逆问题的大小和材料中的潜在不连续性。使用信赖域反射算法（一种基于局部梯度的优化方法）最小化FEMU最小二乘目标。通过目标的解析导数和材料延续策略提高计算效率。通过基于合成生成数据的三个数值示例对所提出的框架进行评估：刚性基础上的Canham壳条、人体腹壁的Koiter壳模型的压痕以及Neo-Hookean块的压痕。这些示例验证了所提出方法通过机械接触重建非均匀材料的能力。解析导数提高了计算效率，并便于对材料参数进行灵敏度和可识别性分析。所提出的方法是非破坏性的，可用于各种逆问题，如软组织的体内生物力学和实验室材料表征。
英文摘要
This study presents a contact-based isogeometric Finite Element Model Updating (FEMU) framework for identifying spatially varying constitutive parameters of nonlinear solids. The formulation considers large quasi-static deformations of hyperelastic 3D solids and thin shells due to mechanical contact. The proposed inverse approach utilizes full-field displacement measurements available at least on the free surface and, in the case of pure Dirichlet boundary conditions, the resultant contact forces as well. The nonuniform material parameter fields are discretized using low-order Lagrange interpolation independent of the isogeometric analysis mesh, providing control over the inverse problem size and potential discontinuities in the material. The FEMU least-squares objective is minimized using a trust-region reflective algorithm - a local gradient-based optimization approach. Computational efficiency is enhanced through the analytical derivatives of the objective and a material continuation strategy. The proposed framework is evaluated through three numerical examples based on synthetically generated data: a Canham shell strip on a rigid foundation, indentation of a Koiter shell model of the human abdominal wall, and indentation of a Neo-Hookean block. The examples verify the ability of the proposed method to reconstruct inhomogeneous material via mechanical contact. Analytical derivatives improve the computational efficiency and facilitate conducting sensitivity and identifiability analyses of the material parameters. The presented approach is non-destructive and can be used for various inverse problems, such as in-vivo biomechanics of soft tissues and laboratory material characterization.
