{"title":"为具有尖锐界面的复合材料中脆性裂纹网络的演变建模的正则化变分力学理论","authors":"","doi":"10.1016/j.jmps.2024.105772","DOIUrl":null,"url":null,"abstract":"<div><p>In the design of structural materials, there is traditionally a tradeoff between achieving high strength and achieving high toughness. Nature offers creative solutions to this problem in the form of structural biomaterials (SBs), intelligent arrangements of mineral and organic phases which possess greater strength and toughness than the constituents. The micro-architecture of SBs like nacre and sea sponge spicules are characterized by weak organic interfaces between brittle mineral phases. To better understand the toughening mechanisms in SBs requires simulation techniques which can resolve arbitrary interface and bulk fracture patterns.</p><p>In this work, we present a modified regularization of Variational Fracture Theory (VFT) that allows for simulation of fracture in materials and structures with weak interfaces. The core of our approach is to widen the weak interfaces on a length scale proportional to that of the diffuse damage field, and assign a reduced fracture toughness therein. We show that in 2D the modified regularized functionals <span><math><mi>Γ</mi></math></span>-converge to that for sharp cracks. The resulting thin weak interfaces have fracture toughness which depends on the bulk material fracture toughness, the widened interface fracture toughness, and the ratio of the widened interface length scale to the crack regularization length scale. We next apply our modified regularization within a computer implementation of regularized VFT, which we term RVFTI. We assess the performance of RVFTI in 2D by reproducing the effective interface fracture toughness predicted by the <span><math><mi>Γ</mi></math></span>-convergence theory and simulating crack trapping at a bi-material interface. We then use RVFTI to study toughening in SB-inspired microarchitectures, namely layered materials and materials with wavy interfaces.</p></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":null,"pages":null},"PeriodicalIF":5.0000,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A regularized variational mechanics theory for modeling the evolution of brittle crack networks in composite materials with sharp interfaces\",\"authors\":\"\",\"doi\":\"10.1016/j.jmps.2024.105772\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In the design of structural materials, there is traditionally a tradeoff between achieving high strength and achieving high toughness. Nature offers creative solutions to this problem in the form of structural biomaterials (SBs), intelligent arrangements of mineral and organic phases which possess greater strength and toughness than the constituents. The micro-architecture of SBs like nacre and sea sponge spicules are characterized by weak organic interfaces between brittle mineral phases. To better understand the toughening mechanisms in SBs requires simulation techniques which can resolve arbitrary interface and bulk fracture patterns.</p><p>In this work, we present a modified regularization of Variational Fracture Theory (VFT) that allows for simulation of fracture in materials and structures with weak interfaces. The core of our approach is to widen the weak interfaces on a length scale proportional to that of the diffuse damage field, and assign a reduced fracture toughness therein. We show that in 2D the modified regularized functionals <span><math><mi>Γ</mi></math></span>-converge to that for sharp cracks. The resulting thin weak interfaces have fracture toughness which depends on the bulk material fracture toughness, the widened interface fracture toughness, and the ratio of the widened interface length scale to the crack regularization length scale. We next apply our modified regularization within a computer implementation of regularized VFT, which we term RVFTI. We assess the performance of RVFTI in 2D by reproducing the effective interface fracture toughness predicted by the <span><math><mi>Γ</mi></math></span>-convergence theory and simulating crack trapping at a bi-material interface. We then use RVFTI to study toughening in SB-inspired microarchitectures, namely layered materials and materials with wavy interfaces.</p></div>\",\"PeriodicalId\":17331,\"journal\":{\"name\":\"Journal of The Mechanics and Physics of Solids\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":5.0000,\"publicationDate\":\"2024-08-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"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/S0022509624002382\",\"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}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of The Mechanics and Physics of Solids","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022509624002382","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}
A regularized variational mechanics theory for modeling the evolution of brittle crack networks in composite materials with sharp interfaces
In the design of structural materials, there is traditionally a tradeoff between achieving high strength and achieving high toughness. Nature offers creative solutions to this problem in the form of structural biomaterials (SBs), intelligent arrangements of mineral and organic phases which possess greater strength and toughness than the constituents. The micro-architecture of SBs like nacre and sea sponge spicules are characterized by weak organic interfaces between brittle mineral phases. To better understand the toughening mechanisms in SBs requires simulation techniques which can resolve arbitrary interface and bulk fracture patterns.
In this work, we present a modified regularization of Variational Fracture Theory (VFT) that allows for simulation of fracture in materials and structures with weak interfaces. The core of our approach is to widen the weak interfaces on a length scale proportional to that of the diffuse damage field, and assign a reduced fracture toughness therein. We show that in 2D the modified regularized functionals -converge to that for sharp cracks. The resulting thin weak interfaces have fracture toughness which depends on the bulk material fracture toughness, the widened interface fracture toughness, and the ratio of the widened interface length scale to the crack regularization length scale. We next apply our modified regularization within a computer implementation of regularized VFT, which we term RVFTI. We assess the performance of RVFTI in 2D by reproducing the effective interface fracture toughness predicted by the -convergence theory and simulating crack trapping at a bi-material interface. We then use RVFTI to study toughening in SB-inspired microarchitectures, namely layered materials and materials with wavy interfaces.
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.