弹粘塑性材料单侧约束拟静态接触问题
Quasistatic contact problem with unilateral constraint for elastic-viscoplastic materials
摘要：
本文分下列两部分:1.在第一部分中，我们证明了具有历史依赖算子的抽象变分-半变分不等式的唯一性。该证明是基于静态变分-半变分不等式的已有结果和不动点定理.在第二部分中，我们考虑了一个描述变形体与刚性基础之间的准静态摩擦接触的数学模型。在该模型中，材料行为由弹粘塑性本构定律模拟。该接触模型用法向阻尼响应、单向约束和记忆项描述。在对该模型的分析中，我们使用了本文第一部分的抽象结果。
英文摘要：
This paper consists of two parts. In the first part we prove the unique solvability for the abstract variational-hemivariational inequality with history-dependent operator. The proof is based on the existing result for the static variational-hemivariational inequality and a fixed point argument. In the second part, we consider a mathematical model which describes quasistatic frictional contact between a deformable body and a rigid foundation. In the model the material behaviour is modelled by an elastic-viscoplastic constitutive law. The contact is described with a normal damped response, unilateral constraint and memory term. In the analysis of this model we use the abstract result from the first part of the paper.
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