{"title":"Quantifying the influence of material randomness on strain response of high temperature strain gauges using stochastic finite element method","authors":"Fengling Zhang, Renjie Li, Yazhi Zhao, Jing Tian, Chunyu Qu","doi":"10.1007/s10999-026-09983-5","DOIUrl":null,"url":null,"abstract":"<div><p>Material properties in multi-layer high temperature strain gauge structures exhibit inherent three-dimensional randomness, leading to variability in strain response even under identical conditions. This paper quantifies the influence of this uncertainty on the strain response of each layer using the stochastic finite element method. Three-dimensional random fields of elastic modulus (<i>E</i>), Poisson’s ratio (<i>ν</i>), and thermal expansion coefficient (<i>α</i>) are discretized via the local average method, and Monte Carlo simulation is employed to obtain response statistics. A hybrid finite element model combining solid elements for bonding layers and beam elements for the sensitive grid is established, with virtual connection elements handling the interface. Static tensile tests with digital image correlation (DIC) are conducted for validation. Results reveal a clear attenuation law: uncertainty decreases as it propagates from the specimen to the sensitive grid (<i>cov</i>(s<sub>1</sub>)><i>cov</i>(s<sub>2</sub>)><i>cov</i>(s<sub>3</sub>)><i>cov</i>(s<sub>4</sub>)). The uncertainty of the specimen’s material parameters dominates the grid’s strain response, while the grid’s own parameter uncertainty is negligible. Under high temperature conditions (1000 °C), α uncertainty has an order-of-magnitude greater influence than <i>E</i> and <i>ν</i>. DIC results confirm the uncertainty propagation trend and the decrease in mean strain with increasing bonding layer thickness, providing theoretical guidance for installation process optimization and measurement reliability improvement.</p></div>","PeriodicalId":593,"journal":{"name":"International Journal of Mechanics and Materials in Design","volume":"22 3","pages":""},"PeriodicalIF":4.7000,"publicationDate":"2026-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Mechanics and Materials in Design","FirstCategoryId":"88","ListUrlMain":"https://link.springer.com/article/10.1007/s10999-026-09983-5","RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
引用次数: 0
Abstract
Material properties in multi-layer high temperature strain gauge structures exhibit inherent three-dimensional randomness, leading to variability in strain response even under identical conditions. This paper quantifies the influence of this uncertainty on the strain response of each layer using the stochastic finite element method. Three-dimensional random fields of elastic modulus (E), Poisson’s ratio (ν), and thermal expansion coefficient (α) are discretized via the local average method, and Monte Carlo simulation is employed to obtain response statistics. A hybrid finite element model combining solid elements for bonding layers and beam elements for the sensitive grid is established, with virtual connection elements handling the interface. Static tensile tests with digital image correlation (DIC) are conducted for validation. Results reveal a clear attenuation law: uncertainty decreases as it propagates from the specimen to the sensitive grid (cov(s1)>cov(s2)>cov(s3)>cov(s4)). The uncertainty of the specimen’s material parameters dominates the grid’s strain response, while the grid’s own parameter uncertainty is negligible. Under high temperature conditions (1000 °C), α uncertainty has an order-of-magnitude greater influence than E and ν. DIC results confirm the uncertainty propagation trend and the decrease in mean strain with increasing bonding layer thickness, providing theoretical guidance for installation process optimization and measurement reliability improvement.
期刊介绍：
It is the objective of this journal to provide an effective medium for the dissemination of recent advances and original works in mechanics and materials'' engineering and their impact on the design process in an integrated, highly focused and coherent format. The goal is to enable mechanical, aeronautical, civil, automotive, biomedical, chemical and nuclear engineers, researchers and scientists to keep abreast of recent developments and exchange ideas on a number of topics relating to the use of mechanics and materials in design.
Analytical synopsis of contents:
The following non-exhaustive list is considered to be within the scope of the International Journal of Mechanics and Materials in Design:
Intelligent Design:
Nano-engineering and Nano-science in Design;
Smart Materials and Adaptive Structures in Design;
Mechanism(s) Design;
Design against Failure;
Design for Manufacturing;
Design of Ultralight Structures;
Design for a Clean Environment;
Impact and Crashworthiness;
Microelectronic Packaging Systems.
Advanced Materials in Design:
Newly Engineered Materials;
Smart Materials and Adaptive Structures;
Micromechanical Modelling of Composites;
Damage Characterisation of Advanced/Traditional Materials;
Alternative Use of Traditional Materials in Design;
Functionally Graded Materials;
Failure Analysis: Fatigue and Fracture;
Multiscale Modelling Concepts and Methodology;
Interfaces, interfacial properties and characterisation.
Design Analysis and Optimisation:
Shape and Topology Optimisation;
Structural Optimisation;
Optimisation Algorithms in Design;
Nonlinear Mechanics in Design;
Novel Numerical Tools in Design;
Geometric Modelling and CAD Tools in Design;
FEM, BEM and Hybrid Methods;
Integrated Computer Aided Design;
Computational Failure Analysis;
Coupled Thermo-Electro-Mechanical Designs.
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