### Numerical Simulation of a Dynamic Contact Issue for Piezoelectric Materials

Youssef Ouafik

#### Abstract

This paper deals with the numerical analysis of a dynamic contact problem with friction between a piezoelectric body and an electrically conductive foundation. The material’s behaviour is described by means of an electro-viscoelastic constitutive law. The contact is modelled using the classical normal damped response condition and a friction law. The mechanical model is described as a coupled system of a nonlinear variational equation for the velocity field and a linear variational equation for the electric potential field. The discrete scheme of the coupled system is introduced based on a finite element method to approximate the spatial variable and an Euler scheme to discretize the time derivate. The frictional contact is treated by using a penalized approach and a version of Newton’s method. A solution algorithm is discussed and implemented. Finally, numerical simulation results are reported on a two-dimensional test problem. These simulations show the performance of the algorithm and illustrate the effects of the conductivity of the foundation, as well.

#### Keywords

Dynamic process; Finite element; Normal damped response; Numerical simulations; Piezoelectric material.

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#### References

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