{"title":"An anisotropic full-network model with damage surface for the Mullins effect in filled rubbers","authors":"Gordon Kumar, Laurence Brassart","doi":"10.1016/j.ijsolstr.2024.113030","DOIUrl":null,"url":null,"abstract":"<div><p>The Mullins effect is a highly anisotropic damage phenomenon exhibited by filled rubbers among other soft materials. When filled rubbers are subjected to uniaxial tension, their apparent stiffness drops in the direction of stretching but is essentially unaltered in the transverse directions. However, micromechanical full-network models where Mullins softening is described at the level of individual chains often predict that uniaxial deformations induce transverse softening in addition to softening in the stretching direction. Moreover, these approaches typically require the storage of damage state variables for each chain, which is computationally expensive. Taking an alternative approach, we present a full-network model for the Mullins effect where the damage state is described by a single macroscopic damage tensor from which the damage state in each direction can be calculated. The evolution of damage is specified through damage surfaces and damage flow rules, which depend on the directions of principal stretches. The model is shown to reproduce experimental data for filled rubbers sequentially subjected to uniaxial tension in different directions. The model is also implemented in the finite element software ABAQUS as a user subroutine UMAT to illustrate the suitability of the model to simulate non-homogeneous deformation states.</p></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"304 ","pages":"Article 113030"},"PeriodicalIF":3.4000,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0020768324003895/pdfft?md5=4f8c59b221fa3ccaf3a269f42217e487&pid=1-s2.0-S0020768324003895-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Solids and Structures","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0020768324003895","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
The Mullins effect is a highly anisotropic damage phenomenon exhibited by filled rubbers among other soft materials. When filled rubbers are subjected to uniaxial tension, their apparent stiffness drops in the direction of stretching but is essentially unaltered in the transverse directions. However, micromechanical full-network models where Mullins softening is described at the level of individual chains often predict that uniaxial deformations induce transverse softening in addition to softening in the stretching direction. Moreover, these approaches typically require the storage of damage state variables for each chain, which is computationally expensive. Taking an alternative approach, we present a full-network model for the Mullins effect where the damage state is described by a single macroscopic damage tensor from which the damage state in each direction can be calculated. The evolution of damage is specified through damage surfaces and damage flow rules, which depend on the directions of principal stretches. The model is shown to reproduce experimental data for filled rubbers sequentially subjected to uniaxial tension in different directions. The model is also implemented in the finite element software ABAQUS as a user subroutine UMAT to illustrate the suitability of the model to simulate non-homogeneous deformation states.
穆林斯效应是填充橡胶和其他软质材料表现出的一种高度各向异性的破坏现象。当填充橡胶受到单轴拉伸时,其表观刚度在拉伸方向上会下降,但在横向方向上基本不会改变。然而,从单链层面描述穆林斯软化的微机械全网络模型通常预测,单轴变形除了会引起拉伸方向的软化外,还会引起横向软化。此外,这些方法通常需要存储每条链的损伤状态变量,计算成本高昂。我们采用另一种方法,为穆林斯效应提出了一个全网络模型,其中的损伤状态由一个单一的宏观损伤张量来描述,通过该张量可以计算出每个方向上的损伤状态。损伤的演变是通过损伤面和损伤流规则来指定的,而损伤面和损伤流规则取决于主拉伸方向。实验表明,该模型重现了填充橡胶在不同方向上连续受到单轴拉伸的实验数据。该模型还作为 UMAT 用户子程序在有限元软件 ABAQUS 中实施,以说明该模型适用于模拟非均质变形状态。
期刊介绍:
The International Journal of Solids and Structures has as its objective the publication and dissemination of original research in Mechanics of Solids and Structures as a field of Applied Science and Engineering. It fosters thus the exchange of ideas among workers in different parts of the world and also among workers who emphasize different aspects of the foundations and applications of the field.
Standing as it does at the cross-roads of Materials Science, Life Sciences, Mathematics, Physics and Engineering Design, the Mechanics of Solids and Structures is experiencing considerable growth as a result of recent technological advances. The Journal, by providing an international medium of communication, is encouraging this growth and is encompassing all aspects of the field from the more classical problems of structural analysis to mechanics of solids continually interacting with other media and including fracture, flow, wave propagation, heat transfer, thermal effects in solids, optimum design methods, model analysis, structural topology and numerical techniques. Interest extends to both inorganic and organic solids and structures.