Quasistatic Bilateral Contact Problem With Adhesion and Nonlocal Friction for Viscoelastic Materials
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摘要: 建立了描述变形体和基础间接触问题的数学模型.接触是双面的,并采用非局部摩擦定理建模,支承列入计算.粘结场(bonding field)的变化用一个一阶的常微分方程来表示,材料特性用一个非线性粘弹性本构关系建模.导出了该力学问题的变分公式,当摩擦因数充分小时,证明了其弱解的存在性和唯一性.依赖于时间的变分不等式、微分方程和Banach不动点理论,是该证明依据的基础.Abstract: A mathematical model which describes a contact problem between a de form able body and a foundation was considered. The contact was bilateral and was modelled with non local friction law in which adhesion was taken in to account. The evolution of the bonding field was described by a firstorder differential equation and the material. s behavior was modelled with an on linear viscoe lastic constitutive law. A variational formulation of the mechanical problem was derived and the existence and uniqueness result of the weak so lution were proved if the coefficien to ffriction was sufficiently small. The proof is based on arguments of time-dependent variationa line qualities, differential equations and Banach fixed-point theorem.
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Key words:
- viscoelastic materials /
- adhesions /
- nonlocal friction /
- fixed point /
- weak solution
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