{"title":"Stability and crack nucleation in variational phase-field models of fracture: Effects of length-scales and stress multi-axiality","authors":"","doi":"10.1016/j.jmps.2024.105802","DOIUrl":null,"url":null,"abstract":"<div><p>We investigate the conditions for crack nucleation in variational gradient damage models used as phase-field models of brittle and cohesive fracture. Viewing crack nucleation as a structural stability problem, we analyze how solutions with diffuse damage become unstable and bifurcate towards localized states, representing the smeared version of cracks. We consider gradient damage models with a linear softening response, incorporating distinct softening parameters for the spherical and deviatoric modes. These parameters are employed to adjust the peak pressure and shear stress, resulting in an equivalent cohesive behavior. Through analytical and numerical second-order stability and bifurcation analyses, we characterize the crack nucleation conditions in quasi-static, rate-independent evolutions governed by a local energy minimization principle. We assess the stability of crack development, determining whether it is preceded by a stable phase with diffuse damage or not. Our results quantitatively characterize the classical transition between brittle and cohesive-like behaviors. A fully analytical solution for a one-dimensional problem provides a clear illustration of the complex bifurcation and instability phenomena, underpinning their connection with classical energetic arguments. The stability analysis under multi-axial loading reveals a fundamental non-trivial influence of the loading mode on the critical load for crack nucleation. We show that volumetric-dominated deformation mode can remain stable in the softening regime, thus delaying crack nucleation after the peak stress. This feature depends only on the properties of the local response of the material and is insensitive to structural scale effects. Our findings disclose the subtle interplay among the regularization length, the material’s cohesive length-scale, structural size, and the loading mode to determine the crack nucleation conditions and the effective strength of phase-field models of fracture.</p></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":null,"pages":null},"PeriodicalIF":5.0000,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022509624002680/pdfft?md5=3f8e20c69f289c23a5519fae58aa6d70&pid=1-s2.0-S0022509624002680-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/S0022509624002680","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
We investigate the conditions for crack nucleation in variational gradient damage models used as phase-field models of brittle and cohesive fracture. Viewing crack nucleation as a structural stability problem, we analyze how solutions with diffuse damage become unstable and bifurcate towards localized states, representing the smeared version of cracks. We consider gradient damage models with a linear softening response, incorporating distinct softening parameters for the spherical and deviatoric modes. These parameters are employed to adjust the peak pressure and shear stress, resulting in an equivalent cohesive behavior. Through analytical and numerical second-order stability and bifurcation analyses, we characterize the crack nucleation conditions in quasi-static, rate-independent evolutions governed by a local energy minimization principle. We assess the stability of crack development, determining whether it is preceded by a stable phase with diffuse damage or not. Our results quantitatively characterize the classical transition between brittle and cohesive-like behaviors. A fully analytical solution for a one-dimensional problem provides a clear illustration of the complex bifurcation and instability phenomena, underpinning their connection with classical energetic arguments. The stability analysis under multi-axial loading reveals a fundamental non-trivial influence of the loading mode on the critical load for crack nucleation. We show that volumetric-dominated deformation mode can remain stable in the softening regime, thus delaying crack nucleation after the peak stress. This feature depends only on the properties of the local response of the material and is insensitive to structural scale effects. Our findings disclose the subtle interplay among the regularization length, the material’s cohesive length-scale, structural size, and the loading mode to determine the crack nucleation conditions and the effective strength of phase-field models of fracture.
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.