{"title":"谐波型软材料与刚性楔体相互作用的应力奇点","authors":"Kui Miao, Qiang Zhang, Ming Dai, Cun-Fa Gao","doi":"10.1016/j.engfracmech.2025.111576","DOIUrl":null,"url":null,"abstract":"<div><div>Composite structures of rigid wedges embedded in soft elastic materials are prevalent in biomedical devices, soft robotics, and flexible electronics. Due to significant mismatches in the elastic moduli between soft materials and rigid wedges, severe stress concentrations may occur in the vicinity of the wedge corner, which may further lead to certain structural failure such as rupture of the soft matrices. The interactions between soft matrices and rigid wedges have been widely studied in the literature but mainly in the context of linear elasticity and small deformation assumptions. Relevant studies about rigid wedges embedded in soft materials exhibiting geometric and constitutive nonlinearities are extremely limited and it remains unclear whether the equations and conclusions in linear elasticity are still applicable. In this paper, we present an asymptotic analysis of the local elastostatic field for the case of a rigid wedge perfectly bonded to a soft rubber-like matrix which is modelled as a hyperelastic material of harmonic type under large deformations. The asymptotic results demonstrate that the singularity behavior of the local stress and deformation gradient near the wedge corner depend solely on the angle of the wedge (which is in sharp contrast to corresponding linear elasticity-based results). In addition, we show that asymptotic singular solutions for the current hyperelastic case are conditional on the angle of the wedge (they exist only for a specific range of the angle of the wedge), indicating that severe volumetric distortion may occur in the vicinity of the wedge corner for certain acute angles of the wedge (which fails to be captured with the use of linear elasticity theory).</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"328 ","pages":"Article 111576"},"PeriodicalIF":5.3000,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Stress singularities in soft materials of harmonic type interacting with a rigid wedge\",\"authors\":\"Kui Miao, Qiang Zhang, Ming Dai, Cun-Fa Gao\",\"doi\":\"10.1016/j.engfracmech.2025.111576\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Composite structures of rigid wedges embedded in soft elastic materials are prevalent in biomedical devices, soft robotics, and flexible electronics. Due to significant mismatches in the elastic moduli between soft materials and rigid wedges, severe stress concentrations may occur in the vicinity of the wedge corner, which may further lead to certain structural failure such as rupture of the soft matrices. The interactions between soft matrices and rigid wedges have been widely studied in the literature but mainly in the context of linear elasticity and small deformation assumptions. Relevant studies about rigid wedges embedded in soft materials exhibiting geometric and constitutive nonlinearities are extremely limited and it remains unclear whether the equations and conclusions in linear elasticity are still applicable. In this paper, we present an asymptotic analysis of the local elastostatic field for the case of a rigid wedge perfectly bonded to a soft rubber-like matrix which is modelled as a hyperelastic material of harmonic type under large deformations. The asymptotic results demonstrate that the singularity behavior of the local stress and deformation gradient near the wedge corner depend solely on the angle of the wedge (which is in sharp contrast to corresponding linear elasticity-based results). In addition, we show that asymptotic singular solutions for the current hyperelastic case are conditional on the angle of the wedge (they exist only for a specific range of the angle of the wedge), indicating that severe volumetric distortion may occur in the vicinity of the wedge corner for certain acute angles of the wedge (which fails to be captured with the use of linear elasticity theory).</div></div>\",\"PeriodicalId\":11576,\"journal\":{\"name\":\"Engineering Fracture Mechanics\",\"volume\":\"328 \",\"pages\":\"Article 111576\"},\"PeriodicalIF\":5.3000,\"publicationDate\":\"2025-09-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Engineering Fracture Mechanics\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0013794425007775\",\"RegionNum\":2,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Engineering Fracture Mechanics","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0013794425007775","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MECHANICS","Score":null,"Total":0}
Stress singularities in soft materials of harmonic type interacting with a rigid wedge
Composite structures of rigid wedges embedded in soft elastic materials are prevalent in biomedical devices, soft robotics, and flexible electronics. Due to significant mismatches in the elastic moduli between soft materials and rigid wedges, severe stress concentrations may occur in the vicinity of the wedge corner, which may further lead to certain structural failure such as rupture of the soft matrices. The interactions between soft matrices and rigid wedges have been widely studied in the literature but mainly in the context of linear elasticity and small deformation assumptions. Relevant studies about rigid wedges embedded in soft materials exhibiting geometric and constitutive nonlinearities are extremely limited and it remains unclear whether the equations and conclusions in linear elasticity are still applicable. In this paper, we present an asymptotic analysis of the local elastostatic field for the case of a rigid wedge perfectly bonded to a soft rubber-like matrix which is modelled as a hyperelastic material of harmonic type under large deformations. The asymptotic results demonstrate that the singularity behavior of the local stress and deformation gradient near the wedge corner depend solely on the angle of the wedge (which is in sharp contrast to corresponding linear elasticity-based results). In addition, we show that asymptotic singular solutions for the current hyperelastic case are conditional on the angle of the wedge (they exist only for a specific range of the angle of the wedge), indicating that severe volumetric distortion may occur in the vicinity of the wedge corner for certain acute angles of the wedge (which fails to be captured with the use of linear elasticity theory).
期刊介绍:
EFM covers a broad range of topics in fracture mechanics to be of interest and use to both researchers and practitioners. Contributions are welcome which address the fracture behavior of conventional engineering material systems as well as newly emerging material systems. Contributions on developments in the areas of mechanics and materials science strongly related to fracture mechanics are also welcome. Papers on fatigue are welcome if they treat the fatigue process using the methods of fracture mechanics.