{"title":"Hyperinelasticity: An energy-based constitutive modelling approach to isothermal large inelastic deformation of polymers. Part I","authors":"","doi":"10.1016/j.jmps.2024.105790","DOIUrl":null,"url":null,"abstract":"<div><p>The foundation of a new concept, coined here as <em>hyperinelasticity</em>, is presented in this work for modelling the isothermal elastic and inelastic behaviours of polymers. This concept is based on the premise that both the elastic and inelastic behaviours of the subject specimen in the primary loading path may be characterised by a single constitutive law derived from a comprehensive deformation energy <span><math><mi>W</mi></math></span>, akin to hyperelasticity, whose constitutive parameters determine and capture both the elastic and inelastic behaviours without the need for additional flow/yield/damage parameters. This <em>core</em> hyperinelastic model captures the elastic and inelastic behaviours in the primary loading path. It is then further specialised, by augmenting the embedded constitutive parameters in the <em>core</em> model, for capturing the inelasticity of the unloading behaviour and the rate of deformation effects. The former is done by devising and incorporating a discontinuous inelasticity variable into the <em>core</em> function, and the latter is achieved by considering that the <em>core</em> model parameters can evolve with, i.e., be a function of, the deformation rate. Examples of the application of the <em>core</em> and <em>augmented</em> hyperinelastic models to a wide range of extant experimental datasets will be presented, ranging from foams, glassy and semi-crystalline polymers to hydrogels and liquid crystal elastomers. The loading modes encompass both tensile and compressive deformations. With a reduced set of number of model parameters (compared with the existing models in the literature), simplicity of implementation (as essentially a straightforward extension to hyperelasticity), and encouraging accuracy in the modelling results, the concept of <em>hyperinelasticity</em> together with the presented hyperinelastic model are proposed as a unified modelling means for capturing the elastic and inelastic behaviours of polymers.</p></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":null,"pages":null},"PeriodicalIF":5.0000,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022509624002564/pdfft?md5=f6b37beb892921440112a82732ab7fb0&pid=1-s2.0-S0022509624002564-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/S0022509624002564","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 foundation of a new concept, coined here as hyperinelasticity, is presented in this work for modelling the isothermal elastic and inelastic behaviours of polymers. This concept is based on the premise that both the elastic and inelastic behaviours of the subject specimen in the primary loading path may be characterised by a single constitutive law derived from a comprehensive deformation energy , akin to hyperelasticity, whose constitutive parameters determine and capture both the elastic and inelastic behaviours without the need for additional flow/yield/damage parameters. This core hyperinelastic model captures the elastic and inelastic behaviours in the primary loading path. It is then further specialised, by augmenting the embedded constitutive parameters in the core model, for capturing the inelasticity of the unloading behaviour and the rate of deformation effects. The former is done by devising and incorporating a discontinuous inelasticity variable into the core function, and the latter is achieved by considering that the core model parameters can evolve with, i.e., be a function of, the deformation rate. Examples of the application of the core and augmented hyperinelastic models to a wide range of extant experimental datasets will be presented, ranging from foams, glassy and semi-crystalline polymers to hydrogels and liquid crystal elastomers. The loading modes encompass both tensile and compressive deformations. With a reduced set of number of model parameters (compared with the existing models in the literature), simplicity of implementation (as essentially a straightforward extension to hyperelasticity), and encouraging accuracy in the modelling results, the concept of hyperinelasticity together with the presented hyperinelastic model are proposed as a unified modelling means for capturing the elastic and inelastic behaviours of polymers.
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.