Crack-face frictional contact modelling in cracked piezoelectric materials

Abstract

Actuators, sensors, micro- and nano-electromechanical systems and other piezoelectirc components are generally constructed in block form or as a thin laminated composites. The study of the integrity of such materials in their various forms and small sizes is still a challenge nowadays. To gain a better understanding of these systems, this work presents a crack surface contact formulation that includes friction and thus makes it possible to study the integrity of these advanced materials under more realistic crack surface multifield operational conditions. The dual boundary element method (BEM) is used for modeling frictional crack surface contact on piezoelectric solids in the presence of electric fields, further taking into account the electrical semipermeable boundary conditions on the crack. The formulation uses contact operators over the augmented Lagrangian to enforce contact constraints on the crack surfaces. The BEM reveals to be a very suitable methodology for these interface interaction problems because it considers only the boundary degrees of freedom, what makes it possible to reduce the number of unknowns and to obtain accurate results with a much lower number of elements than formulations based on the standard finite element method or the eXtended finite element method. The capabilities of this methodology are illustrated by solving some benchmark problems.