{"title":"超弹性。第二部分:基于拉伸的配方","authors":"","doi":"10.1016/j.jmps.2024.105825","DOIUrl":null,"url":null,"abstract":"<div><p>A generalisation of the <em>hyperinelasticity</em> modelling framework devised in Part I of this sequel is formulated here, by presenting a (principal) stretches-based hyperinelastic deformation energy function <span><math><mrow><mi>W</mi><mfenced><mrow><mi>F</mi></mrow></mfenced></mrow></math></span>. This generalisation is based on the premise that the (principal) stretches <span><math><msub><mrow><mi>λ</mi></mrow><mrow><mi>j</mi></mrow></msub></math></span> may assume any arbitrary real-valued exponents, rather than being restricted to the prescriptive powers 2 and −2, as in principal invariants-based models. The motivation behind this extension is to reduce the overall number of model parameters and thereby increase the versatility of the application of the <em>hyperinelasticity</em> framework, as well as to provide a more universal model. The ensuing hyperinelastic model is then applied to a wide range of extant experimental datasets encompassing foams, glassy and semi-crystalline polymers, hydrogels and liquid crystal elastomers, over both elastic and inelastic deformation ranges including yield, softening and plateau, and hardening behaviours, under tensile and compressive deformations. Upon demonstrating the favourable simulation of the foregoing behaviours by the model, its application is then extended to account for other nuanced aspects of inelasticity such as the effects of rate of deformation, crystallinity volume and angle of printing in 3D printed lattice structures. This augmentation is done via devising a generalised modelling framework which allows for the incorporation of a generic tensorial (including rank zero scalar) field of inelasticity-inducing factors into the core model, resulting in the model parameters to evolve with an appropriate measure of the factor of interest; e.g., deformation rate, crystallinity volume ratio etc. The proposed modelling framework will be shown to capture these effects proficiently. Given the simplicity of this modelling approach, as essentially an extension in the application of hyperelasticity, its versatility of implementation, and the favourable capturing of both elastic and inelastic behaviours, the devised <em>hyperinelasticity</em> framework is presented for application to the large elastic and inelastic deformation of polymers and elastomers.</p></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":null,"pages":null},"PeriodicalIF":5.0000,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022509624002916/pdfft?md5=a309fec39d98a6e64c74e2dd44c3ce19&pid=1-s2.0-S0022509624002916-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Hyperinelasticity. 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The motivation behind this extension is to reduce the overall number of model parameters and thereby increase the versatility of the application of the <em>hyperinelasticity</em> framework, as well as to provide a more universal model. The ensuing hyperinelastic model is then applied to a wide range of extant experimental datasets encompassing foams, glassy and semi-crystalline polymers, hydrogels and liquid crystal elastomers, over both elastic and inelastic deformation ranges including yield, softening and plateau, and hardening behaviours, under tensile and compressive deformations. Upon demonstrating the favourable simulation of the foregoing behaviours by the model, its application is then extended to account for other nuanced aspects of inelasticity such as the effects of rate of deformation, crystallinity volume and angle of printing in 3D printed lattice structures. This augmentation is done via devising a generalised modelling framework which allows for the incorporation of a generic tensorial (including rank zero scalar) field of inelasticity-inducing factors into the core model, resulting in the model parameters to evolve with an appropriate measure of the factor of interest; e.g., deformation rate, crystallinity volume ratio etc. The proposed modelling framework will be shown to capture these effects proficiently. Given the simplicity of this modelling approach, as essentially an extension in the application of hyperelasticity, its versatility of implementation, and the favourable capturing of both elastic and inelastic behaviours, the devised <em>hyperinelasticity</em> framework is presented for application to the large elastic and inelastic deformation of polymers and elastomers.</p></div>\",\"PeriodicalId\":17331,\"journal\":{\"name\":\"Journal of The Mechanics and Physics of Solids\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":5.0000,\"publicationDate\":\"2024-08-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0022509624002916/pdfft?md5=a309fec39d98a6e64c74e2dd44c3ce19&pid=1-s2.0-S0022509624002916-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/S0022509624002916\",\"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/S0022509624002916","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}
Hyperinelasticity. Part II: A stretch-based formulation
A generalisation of the hyperinelasticity modelling framework devised in Part I of this sequel is formulated here, by presenting a (principal) stretches-based hyperinelastic deformation energy function . This generalisation is based on the premise that the (principal) stretches may assume any arbitrary real-valued exponents, rather than being restricted to the prescriptive powers 2 and −2, as in principal invariants-based models. The motivation behind this extension is to reduce the overall number of model parameters and thereby increase the versatility of the application of the hyperinelasticity framework, as well as to provide a more universal model. The ensuing hyperinelastic model is then applied to a wide range of extant experimental datasets encompassing foams, glassy and semi-crystalline polymers, hydrogels and liquid crystal elastomers, over both elastic and inelastic deformation ranges including yield, softening and plateau, and hardening behaviours, under tensile and compressive deformations. Upon demonstrating the favourable simulation of the foregoing behaviours by the model, its application is then extended to account for other nuanced aspects of inelasticity such as the effects of rate of deformation, crystallinity volume and angle of printing in 3D printed lattice structures. This augmentation is done via devising a generalised modelling framework which allows for the incorporation of a generic tensorial (including rank zero scalar) field of inelasticity-inducing factors into the core model, resulting in the model parameters to evolve with an appropriate measure of the factor of interest; e.g., deformation rate, crystallinity volume ratio etc. The proposed modelling framework will be shown to capture these effects proficiently. Given the simplicity of this modelling approach, as essentially an extension in the application of hyperelasticity, its versatility of implementation, and the favourable capturing of both elastic and inelastic behaviours, the devised hyperinelasticity framework is presented for application to the large elastic and inelastic deformation of polymers and elastomers.
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.