ANALYSIS OF A DYNAMIC VISCOELASTIC-VISCOPLASTIC PIEZOELECTRIC CONTACT PROBLEM

作者：Campo Marco; Fernandez Jose R^*; Rodriguez Aros Angel D; Rodriguez Jose M

来源：ESAIM: Mathematical Modelling and Numerical Analysis , 2017, 51(2): 565-586.

DOI：10.1051/m2an/2016027

• Viscoelasticity
• viscoplasticity
• piezoelectricity
• existence and uniqueness
• a priori error estimates
• numerical simulations

In this paper, we study, from both variational and numerical points of view, a dynamic contact problem between a viscoelastic-viscoplastic piezoelectric body and a deformable obstacle. The contact is modelled using the classical normal compliance contact condition. The variational formulation is written as a nonlinear ordinary differential equation for the stress field, a nonlinear hyperbolic variational equation for the displacement field and a linear variational equation for the electric potential field. An existence and uniqueness result is proved using Gronwall's lemma, adequate auxiliary problems and fixed-point arguments. Then, fully discrete approximations are introduced using an Euler scheme and the finite element method, for which some a priori error estimates are derived, leading to the linear convergence of the algorithm under suitable additional regularity conditions. Finally, some two-dimensional numerical simulations are presented to show the accuracy of the algorithm and the behaviour of the solution.

• 出版日期2017-4