We consider a general mathematical model which describes the quasistatic contact of a deformable body with an obstacle, the so-called foundation. The material’s behaviour is modeled with a visco-elastic-type constitutive law and the contact is described with a general interface law associated to a version of Coulomb’s law of dry friction. We list the assumptions on the data and provide relevant examples of constitutive laws and boundary conditions. Then, we derive two different variational formulations of the model in which the unknowns are the displacement and the strain field, respectively. We prove the equivalence of these formulations. Finally, we use recent arguments of sweeping process in order to obtain the existence of a unique weak solution to the contact model.

我们考虑一个通用数学模型，该模型描述了可变形体与障碍物（即所谓的基础）的准静态接触。材料的行为用粘弹性型本构定律建模，接触用与库仑干摩擦定律版本相关的一般界面定律描述。我们列出了对数据的假设，并提供了本构定律和边界条件的相关示例。然后，我们推导出模型的两种不同的变分公式，其中未知数分别是位移和应变场。我们证明了这些公式的等价性。最后，我们使用扫描过程的最新参数来获得接触模型的唯一弱解的存在。