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

Bartłomiej Łazorczyk; Roger A. Sauer

Home/Archive/arXiv

arXiv · 2607.18156

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

Bartłomiej Łazorczyk·Roger A. Sauer

View original source ↗Read source document ↗Export metadata ↓

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.

Explore related subjects

cs.CE

Keep this discovery

BibTeX RIS

Bartłomiej Łazorczyk, Roger A. Sauer. 2026-07-20. Contact-based inverse analysis for nonlinear material identification in spatially heterogeneous solids. https://arxiv.org/abs/2607.18156

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

A Framework for Discharge Time Prediction of Energy Storage Units Based on Coupled Dynamics and Multi-Factor Aging Models

This paper presents a physically interpretable framework for predicting time to empty (TTE) in portable embedded systems. The framework couples usage-driven load-power decomposition, electrical power-voltage-current closure, a semi-empirical aging model, and SOC-temperature dynamics. Smartphone telemetry is mapped to battery current through an interpretable load model and conversion-efficiency correction. Battery capacity loss is modeled by combining Arrhenius temperature dependence, SEI diffusion behavior, and cycle-related power-law degradation. The coupled dynamic model then predicts TTE under different initial SOC values, ambient temperatures, and usage profiles. Chronological hold-out evaluation on a 6.9-h smartphone discharge session yielded a current RMSE of 0.0095 $\pm$ 0.0006 A, a temperature RMSE of 2.93 $\pm$ 0.24$^\circ$C, and a TTE MAPE of 4.81 $\pm$ 0.61%. Evaluation on NASA cell B0005 produced a capacity-loss RMSE of 0.031 Ah. Baseline, ablation, and counterfactual analyses further illustrate the contributions of thermal and aging corrections and the relative influence of load features. The results demonstrate the feasibility and interpretability of the proposed framework, while broader validation across devices and batteries remains necessary.

cs.CE↗

arXiv2026

Node-Shift-Encoding Genetic Algorithm with fuzzy-enhanced reference tour to solve the bi-objective service-oriented TSP

The Travelling Salesman Problem (TSP) remains a key area of research in combinatorial optimization, with applications in logistics, manufacturing, and service delivery. This paper addresses a bi-objective service-oriented TSP in which the clients' ranks in the delivery path matter. Unlike conventional depot-based TSP formulations, the considered problem does not assume a distinguished depot or a fixed tour origin. To address this setting, we adapt the Miller--Tucker--Zemlin (MTZ)-based formulation and derive an original linearization of the resulting model, enabling its solution with off-the-shelf integer linear programming solvers. This adaptation avoids the rigid tour origin imposed by the conventional MTZ formulation, for which fixing the starting node does not affect the tour cost but can affect the objective in a customer-rank-sensitive TSP. To solve this problem, we present a Node-Shift-Encoding (NSE)-based Genetic Algorithm augmented with fuzzy reasoning to update the reference tour throughout the evolutionary process. Experimental evaluation on TSPLIB benchmarks demonstrates that the proposed method achieves improved performance compared with the classical NSE approach.

cs.CE↗

arXiv2026

Geometric organization of olfactory descriptor data in the Poincar\'e disk

Odor quality is commonly represented using high dimensional descriptor profiles, yet their low dimensional organization remains unclear. We investigated whether a two-dimensional hyperbolic embedding can provide an interpretable representation of this structure. We applied hyperbolic metric multidimensional scaling to two complementary datasets: 480 Sagar rating profiles from three participants rating 160 odorants on 15 continuous descriptors, and 4983 GoodScents--Leffingwell molecules annotated with 138 binary descriptors. The embeddings substantially preserved pairwise descriptor distances, supporting subsequent analyses of radial and angular organization. In Sagar, rating profile entropy was strongly and negatively associated with hyperbolic radius, with diffuse profiles closer to the center and concentrated profiles closer to the boundary. This radial organization emerged primarily at the level of the full descriptor profile, rather than any individual descriptor, and remained robust across alternative descriptor representations, participant specific analyses, and averaged ratings. Sweet, musky, fruity, pleasantness showed the strongest directional trends. In GoodScents--Leffingwell, active label entropy, reflecting descriptor multiplicity, increased with radius, whereas orthogonalized descriptor entropy, reflecting spread across orthogonal modes, decreased with radius. Related binary descriptors occupied coherent localized high-density regions. These findings reveal complementary radial and angular organization in the hyperbolic representation of olfactory descriptor data. They support hyperbolic mapping as an interpretable descriptive framework in which radius summarizes global profile properties, while the angular component captures continuous descriptor gradients and categorical organization.

cs.CE↗