Contact-based inverse analysis for nonlinear material identification in spatially heterogeneous solids
2026-07-20 • Computational Engineering, Finance, and Science
Computational Engineering, Finance, and Science
AI summaryⓘ
The authors developed a method to figure out how materials that can stretch and bend behave differently in different parts by pressing on them and measuring how they move. They use a special math model that works for complex 3D shapes and thin shells, and they include how the materials touch other objects. Their technique relies on surface movement data and, when available, contact force measurements. They tested their method on computer simulations of different materials and showed it can accurately find where material properties change. This approach can help study soft tissues in the body or materials in labs without damaging them.
isogeometric analysisfinite element model updatinghyperelasticityquasi-static deformationcontact mechanicsinverse problemsLagrange interpolationtrust-region reflective algorithmNeo-Hookean materialsensitivity analysis
Authors
Bartłomiej Łazorczyk, Roger A. Sauer
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.