Existence of a class of variational inequalities modelling quasi-static viscoelastic contact problems
Existence of a class of variational inequalities modelling quasi-static viscoelastic contact problems
复制标题
模拟准静态粘弹性接触问题的一类变分不等式的存在性
DOI：
10.1002/zamm.201800172
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Peng Zijia
中科院分区：
文献类型：
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作者：
Peng Zijia
本文研究粘弹性材料的准静摩擦接触问题中一类变分不等式的存在性。首先考虑由演化变分不等式描述的惯性项参数较小的动态接触问题。然后研究了它们的解在参数趋于零时的渐近行为。基于时间离散化技术和单调算子理论，在演化三元组的框架中以演化包涵的形式求解了这些不等式。我们证明了动态问题的极限函数是准静态变分不等式的解。将抽象结果应用于具有多值本构律和法向阻尼响应的摩擦接触问题。此外，对非单调边界问题也作了一些评述。
This work concerns the existence for a class of variational inequalities arising in quasi‐static frictional contact problems for viscoelastic materials. We first consider dynamic contact problems described by evolutionary variational inequalities with a small parameter in the inertial term. Then we study the asymptotic behavior of their solutions when the parameter tends to zero. Based on a time‐discretization technique and monotone operators theory, the inequalities are solved in the form of evolutionary inclusions in the framework of evolution triples. We show that the limit functions of dynamic problems are solutions to the quasi‐static variational inequalities. Applications of the abstract result to frictional contact problems with multivalued constitutive law and normal damped response are given. Moreover, some comments on nonmonotone boundary problem are presented.