摘要
通过构建一个热耦合的多轴可压缩应变能函数,得到应力-应变、应力-温度和应变-温度之间的函数关系,建立形状记忆聚合物的本构方程.论文引入三个基于对数应变的不变量使得模型(i)可以模拟可压缩情况;(ii)适用于单轴拉伸和等双轴拉伸至少两个基准实验;(iii)多轴有效.通过显式方法(i)给出自由能和熵的具体表达,证明模型热力学定律;(ii)给出应变-应力,温度-应力以及,温度-应变的形函数具体表达.多轴模型在特定的情况下可以自动退化到各自的单轴情况.通过调节形函数的参数,最终得到的模型结果和实验结果能够精确匹配.新方法建立的本构模型得到的结果能更加准确地指导形状记忆聚合物的工程设计.
Shape memory polymer(SMP) has drawn much attention for its abilities in shape fixing and shape recovery triggered by external stimuli(e.g., heat, electric field, magnetic field, irradiation, etc.), and is widely used in aerospace industry, biomedicine field, textile industry, and so on. The majority of the research efforts on SMPs carried out in the past have been concentrated on experimental work, such as improving performance by adding new chemical compositions, and exploring new application for SMP-based elements. Few studies have been committed to establish the constitutive equations of SMPs. However, the constitutive model of SMP is necessary for the design of SMP-based element. Towards this goal, a constitutive model for SMP is established by constructing a multi-axial compressible strain energy function with thermal-coupled property to obtain the stress-strain, stress-temperature and strain-temperature relationships. Three invariants based on the Hencky strain are introduced to make the new model compressible, multi-axial and applicable for at least two different deformation modes, i.e., uniaxial tension and compression and bi-axial tension. Novel points of this paper are presented in four aspects:(i) A thermal-coupled strain energy function is constructed by combining several one-dimensional shape functions via the bridging method with specific invariants.(ii) Explicit forms of Helmholtz free energy and specific entropy are presented for this new model to meet the Clausius-Duhem inequality(i.e., thermomechanical conditions).(iii) The parameters in the shape functions can be explicitly determined without considering complex iteration procedures or switching conditions.(iv) Both thermomechanical cyclic test and stress-recovery test can be simulated by this new model. The new constitutive equations can automatically reduce to the one-dimensional case, and explicit results can be obtained in the uniaxial case or bi-axial case. The modeling results are in good accordance with classical test data. The new const
作者
王晓明
肖衡
Xiaoming Wang;Heng Xiao(School of Civil Engineering,Ningbo Polytechnic,Ningbo,315000;School of Mechanics and Civil Engineering,Jinan University,Guangzhou,510632)
出处
《固体力学学报》
CAS
CSCD
北大核心
2020年第4期366-378,共13页
Chinese Journal of Solid Mechanics
基金
宁波职业技术学院2020年度课题(NZ20C004)资助。
关键词
热耦合
应变能函数
形函数
显式
热力学定律
thermal-coupled
strain energy
shape function
explicit
thermodynamic conditions
