We consider a mathematical model which describes the dynamic process of contact between a piezoelectric body and an electrically conductive foundation. We model the material’s behavior with a nonlinear electro-viscoelastic constitutive law; the contact is frictionless and is described with the normal compliance condition. We derive variational formulation for the model which is in the form of a system involving the displacement field, the electric potential field, the damage field and the adhesion field. We prove the existence of a unique weak solution to the problem. The proof is based on arguments of time dependent variational inequalities, parabolic inequalities, differential equations and fixed point.

中文翻译：

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电粘弹性材料的动态接触问题分析

我们考虑一个数学模型，该模型描述了压电体与导电基础之间接触的动态过程。我们用非线性电粘弹性本构律对材料的行为进行建模。接触是无摩擦的，并以正常的顺应性条件进行描述。我们以包含位移场，电势场，损伤场和粘附场的系统形式得出模型的变分公式。我们证明存在唯一的弱解决方案。该证明基于与时间相关的变分不等式，抛物线不等式，微分方程和不动点的参数。