Analysis and numerical approach for a nonlinear contact problem with non-local friction in piezoelectricity

A mathematical model which describes a frictional contact problem between a piezoelectric body and an electrically conductive foundation is considered. The constitutive relation of the material is assumed to be electro-elastic and involves the nonlinear elastic constitutive Hencky’s law. The contact...

Full description

Saved in:
Bibliographic Details
Published in:Acta mechanica 2021-11, Vol.232 (11), p.4273-4288
Main Authors: Benkhira, El-H., Fakhar, R., Mandyly, Y.
Format: Article
Language:English
Subjects:
Analysis
Classical and Continuum Physics
Coefficient of friction
Constitutive relationships
Control
Dynamical Systems
Electric contacts
Electric properties
Electrical conductivity
Electrical resistivity
Engineering
Engineering Fluid Dynamics
Engineering Thermodynamics
Friction
Heat and Mass Transfer
Iterative methods
Laboratories
Laws, regulations and rules
Mathematical models
Original Paper
Piezoelectricity
Solid Mechanics
Theoretical and Applied Mechanics
Variables
Vibration
Viscoelasticity
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:A mathematical model which describes a frictional contact problem between a piezoelectric body and an electrically conductive foundation is considered. The constitutive relation of the material is assumed to be electro-elastic and involves the nonlinear elastic constitutive Hencky’s law. The contact is modeled with Signorini’s conditions, a version of Coulomb’s law in which the coefficient of friction depends on the slip and a regularized electrical conductivity condition. A variational formulation for the problem is derived; then, the existence of a unique weak solution to the model is proved. Afterward, to solve the problem numerically, a successive iteration technique is proposed, and its convergence is established. Then, a variant of the augmented Lagrangian, the so-called alternating direction method of multipliers, is used to decompose the original problem into two sub-problems, solve them sequentially and update the dual variables at each iteration. Finally, to study the influence of the foundation’s conductivity on the iterative process, numerical experiments of two-dimensional test problems are carried out.
ISSN:0001-5970
1619-6937
DOI:10.1007/s00707-021-03057-7