{"title":"A direct method to identify Young’s moduli and boundary conditions of the heterogeneous material","authors":"","doi":"10.1016/j.ijmecsci.2024.109777","DOIUrl":null,"url":null,"abstract":"<div><div>Identifying unknown Young’s moduli and boundary conditions of the heterogeneous material using locally observed boundary data is the inverse problem which is generally solved by iterative methods. In this paper, a two-steps direct method is proposed for the first time to solve this inverse problem without iterations. The proposed method innovatively decomposes the heterogeneous elasticity inverse problem to two homogeneous elasticity sub-inverse problems. The single-data and multiple-data based direct methods are applied to identify background Young’s modulus and displacement boundary conditions, while the Maxwell–Betti principle based direct method and the equivalent boundary force based direct method are proposed to identify Young’s moduli of inclusions. In addition, an optimal experimental design method with a goal-oriented criterion is proposed to improve the accuracy of the two-steps direct method by optimizing the force application positions in observation data acquisition. Both numerical and physical experiments were conducted. The results demonstrate the feasibility of the proposed two-steps direct method and its optimal experimental design method.</div></div>","PeriodicalId":56287,"journal":{"name":"International Journal of Mechanical Sciences","volume":null,"pages":null},"PeriodicalIF":7.1000,"publicationDate":"2024-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Mechanical Sciences","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S002074032400818X","RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
引用次数: 0
Abstract
Identifying unknown Young’s moduli and boundary conditions of the heterogeneous material using locally observed boundary data is the inverse problem which is generally solved by iterative methods. In this paper, a two-steps direct method is proposed for the first time to solve this inverse problem without iterations. The proposed method innovatively decomposes the heterogeneous elasticity inverse problem to two homogeneous elasticity sub-inverse problems. The single-data and multiple-data based direct methods are applied to identify background Young’s modulus and displacement boundary conditions, while the Maxwell–Betti principle based direct method and the equivalent boundary force based direct method are proposed to identify Young’s moduli of inclusions. In addition, an optimal experimental design method with a goal-oriented criterion is proposed to improve the accuracy of the two-steps direct method by optimizing the force application positions in observation data acquisition. Both numerical and physical experiments were conducted. The results demonstrate the feasibility of the proposed two-steps direct method and its optimal experimental design method.
期刊介绍:
The International Journal of Mechanical Sciences (IJMS) serves as a global platform for the publication and dissemination of original research that contributes to a deeper scientific understanding of the fundamental disciplines within mechanical, civil, and material engineering.
The primary focus of IJMS is to showcase innovative and ground-breaking work that utilizes analytical and computational modeling techniques, such as Finite Element Method (FEM), Boundary Element Method (BEM), and mesh-free methods, among others. These modeling methods are applied to diverse fields including rigid-body mechanics (e.g., dynamics, vibration, stability), structural mechanics, metal forming, advanced materials (e.g., metals, composites, cellular, smart) behavior and applications, impact mechanics, strain localization, and other nonlinear effects (e.g., large deflections, plasticity, fracture).
Additionally, IJMS covers the realms of fluid mechanics (both external and internal flows), tribology, thermodynamics, and materials processing. These subjects collectively form the core of the journal's content.
In summary, IJMS provides a prestigious platform for researchers to present their original contributions, shedding light on analytical and computational modeling methods in various areas of mechanical engineering, as well as exploring the behavior and application of advanced materials, fluid mechanics, thermodynamics, and materials processing.