{"title":"Recovering Mullins damage hyperelastic behaviour with physics augmented neural networks","authors":"","doi":"10.1016/j.jmps.2024.105839","DOIUrl":null,"url":null,"abstract":"<div><p>The aim of this work is to develop a neural network for modelling incompressible hyperelastic behaviour with isotropic damage, the so-called Mullins effect. This is obtained through the use of feed-forward neural networks with special attention to the architecture of the network in order to fulfil several physical restrictions such as objectivity, polyconvexity, non-negativity, material symmetry and thermodynamic consistency. The result is a compact neural network with few parameters that is able to reconstruct the hyperelastic behaviour with Mullins-type damage. The network is trained with artificially generated plane stress data and even correctly captures the full 3D behaviour with much more complex loading conditions. The energy and stress responses are correctly captured, as well as the evolution of the damage. The resulting neural network can be seamlessly implemented in widely used simulation software. Implementation details are provided and all numerical examples are performed in Abaqus.</p></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":null,"pages":null},"PeriodicalIF":5.0000,"publicationDate":"2024-08-29","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/S0022509624003053","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
The aim of this work is to develop a neural network for modelling incompressible hyperelastic behaviour with isotropic damage, the so-called Mullins effect. This is obtained through the use of feed-forward neural networks with special attention to the architecture of the network in order to fulfil several physical restrictions such as objectivity, polyconvexity, non-negativity, material symmetry and thermodynamic consistency. The result is a compact neural network with few parameters that is able to reconstruct the hyperelastic behaviour with Mullins-type damage. The network is trained with artificially generated plane stress data and even correctly captures the full 3D behaviour with much more complex loading conditions. The energy and stress responses are correctly captured, as well as the evolution of the damage. The resulting neural network can be seamlessly implemented in widely used simulation software. Implementation details are provided and all numerical examples are performed in Abaqus.
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.