{"title":"Cancelling the effect of sharp notches or cracks with graded elastic modulus materials","authors":"","doi":"10.1016/j.jmps.2024.105809","DOIUrl":null,"url":null,"abstract":"<div><p>Recent technologies permit to build materials which have elastic spatially varying modulus which can also imitate solutions adopted in Nature to optimize some structures. It has been shown that for example the stress concentration due to a hole in an infinite plate can be cancelled with a radially varying modulus making it similar to load-bearing bones which seem to resist structural failures even in the presence of blood vessel holes (foramina). Here, we attempt to study the classical problem of a sharp wedge (which includes the important case of a crack) looking for stresses varying as power law of the distance from the notch tip, <span><math><mrow><mi>σ</mi><mo>∼</mo><msup><mrow><mi>r</mi></mrow><mrow><mi>α</mi></mrow></msup></mrow></math></span>, with a modulus varying as <span><math><mrow><mi>E</mi><mo>∼</mo><msup><mrow><mi>r</mi></mrow><mrow><mi>β</mi></mrow></msup></mrow></math></span>. In the inhomogeneous case the order of singularity of the LEFM case decreases if <span><math><mrow><mi>β</mi><mo>></mo><mn>0</mn></mrow></math></span>, as confirmed by FEM investigations. Hence, we can remove stress singularities, which suggests an interesting alternative to the “rounding” of the notch. More in general, since for many materials it has been found that both strength and modulus are power laws of the density, using the so called strength-modulus exponent ratio we can obtain optimal design by keeping the asymptotic stress constantly equal to the strength. The present investigation paves the way for a new optimization strategy in the problems which eliminates size-scale effects due to singular stress fields, with potentially very wide applications.</p></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":null,"pages":null},"PeriodicalIF":5.0000,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022509624002758/pdfft?md5=a166f5b55c7b7ebbcf2f5f6bce5be384&pid=1-s2.0-S0022509624002758-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of The Mechanics and Physics of Solids","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022509624002758","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
Recent technologies permit to build materials which have elastic spatially varying modulus which can also imitate solutions adopted in Nature to optimize some structures. It has been shown that for example the stress concentration due to a hole in an infinite plate can be cancelled with a radially varying modulus making it similar to load-bearing bones which seem to resist structural failures even in the presence of blood vessel holes (foramina). Here, we attempt to study the classical problem of a sharp wedge (which includes the important case of a crack) looking for stresses varying as power law of the distance from the notch tip, , with a modulus varying as . In the inhomogeneous case the order of singularity of the LEFM case decreases if , as confirmed by FEM investigations. Hence, we can remove stress singularities, which suggests an interesting alternative to the “rounding” of the notch. More in general, since for many materials it has been found that both strength and modulus are power laws of the density, using the so called strength-modulus exponent ratio we can obtain optimal design by keeping the asymptotic stress constantly equal to the strength. The present investigation paves the way for a new optimization strategy in the problems which eliminates size-scale effects due to singular stress fields, with potentially very wide applications.
期刊介绍:
The aim of Journal of The Mechanics and Physics of Solids is to publish research of the highest quality and of lasting significance on the mechanics of solids. The scope is broad, from fundamental concepts in mechanics to the analysis of novel phenomena and applications. Solids are interpreted broadly to include both hard and soft materials as well as natural and synthetic structures. The approach can be theoretical, experimental or computational.This research activity sits within engineering science and the allied areas of applied mathematics, materials science, bio-mechanics, applied physics, and geophysics.
The Journal was founded in 1952 by Rodney Hill, who was its Editor-in-Chief until 1968. The topics of interest to the Journal evolve with developments in the subject but its basic ethos remains the same: to publish research of the highest quality relating to the mechanics of solids. Thus, emphasis is placed on the development of fundamental concepts of mechanics and novel applications of these concepts based on theoretical, experimental or computational approaches, drawing upon the various branches of engineering science and the allied areas within applied mathematics, materials science, structural engineering, applied physics, and geophysics.
The main purpose of the Journal is to foster scientific understanding of the processes of deformation and mechanical failure of all solid materials, both technological and natural, and the connections between these processes and their underlying physical mechanisms. In this sense, the content of the Journal should reflect the current state of the discipline in analysis, experimental observation, and numerical simulation. In the interest of achieving this goal, authors are encouraged to consider the significance of their contributions for the field of mechanics and the implications of their results, in addition to describing the details of their work.