Modelling and simulation of a dynamic contact problem in thermo-piezoelectricity

• Published in: Engineering and Applied Science Letters Vol. 4; no. 2; pp. 43 - 52
• Main Author: Ouafik, Youssef
• Format: Journal Article
• Language: English
• Published: 31.12.2021
• ISSN: 2617-9695; 2617-9709
• DOI: 10.30538/psrp-easl2021.0069

In this work, we numerically study a dynamic frictional contact problem between a thermo-piezoelectric body and a conductive foundation. The linear thermo-electro-elastic constitutive law is employed to model the thermo-piezoelectric material. The contact is modelled by the Signorini condition and the friction by the Coulomb law. A frictional heat generation and heat transfer across the contact surface are assumed. The heat exchange coefficient is assumed to depend on contact pressure. 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 thermo-mechanical contact is treated by using an augmented Lagrangian approach. A solution algorithm is discussed and implemented. Numerical simulation results are reported, illustrating the mechanical behavior related to the contact condition.