Contact-based inverse analysis for nonlinear material identification in spatially heterogeneous solids

2026-07-20

AI Summary

This study addresses the challenge of identifying nonlinear, spatially heterogeneous constitutive parameters of solid materials when only surface displacements and contact forces are available. To this end, an efficient inverse method based on isogeometric finite element model updating (FEMU) is proposed. By employing low-order Lagrangian interpolation—decoupled from the analysis mesh—to represent spatially varying material fields, and integrating analytical gradient computation, a material-parameter continuation strategy, and a trust-region reflective optimization algorithm, the approach enables non-destructive, high-fidelity parameter identification. Numerical experiments successfully reconstruct heterogeneous material distributions in three-dimensional hyperelastic solids and thin shells, demonstrating the method’s effectiveness and computational efficiency for applications in soft tissue biomechanics and advanced material characterization.

Abstract

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.

Problem

• inverse analysis
• nonlinear material identification
• spatially heterogeneous solids
• contact mechanics
• constitutive parameters

Innovation

• contact-based inverse analysis
• isogeometric FEMU
• spatially heterogeneous materials
• analytical derivatives
• material parameter identification