### Numerical Simulation of a Thermo-piezoelectric Contact Issue with Tresca’s Friction Law

Youssef Ouafik

#### Abstract

A frictional contact problem between a thermo-piezoelectric body and a thermally conductive foundation is numerically studied in this paper. The material’s behaviour is described by means of a thermo-electro-elastic constitutive law. The process is quasistatic, the contact is bilateral and is associated to Tresca’s law for dry friction. Hybrid formulation is introduced, it is a coupled system for the displacement field, the electric potential, the temperature and two Lagrange multipliers. 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 an augmented Lagrangian approach and a version of Newton’s method. A solution algorithm is discussed and implemented. Finally, numerical simulation results are reported. These simulations show the performance of the algorithm and illustrate the effects of the conductivity of the foundation, as well.

#### Keywords

Augmented Lagrangian method; Bilateral contact; Finite element; Quasistatic process; Thermo-piezoelectric material.

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#### References

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