Application of the X-FEM to the fracture of piezoelectric materials

Abstract

Materials exhibiting a strong piezoelectric effect may be used in many applications, where they serve as sensors, actuators or transducers. These applications range from for sub-millimeter length scales in MEMs (Micro-Electro-Mechanical Systems) up to large scales in the the design of smart wings in the aerospace industry. As for regular materials subjected to high mechanical stresses, the knowledge of fracture behavior for these smart materials is often crucial within the design of parts under high electrical and mechanical loading. The Extended Finite Element Method [1] has been originally designed for crack growth analysis in isotropic elastic materials. In association with level-sets [2] as a mean for representing the crack geometry, it is a powerful way to get rid of the costly constrained remeshing needed with conventional techniques. Under certain circumstances, this method is also able to achieve regular convergence rates in the energy error even for a cracked domain [3]. Piezoelectric materials exhibit an transversely isotropic mechanical characteristic, as well as a coupling between mechanical and electrical variables. This leads to different near-crack tip mechanical fields and the presence of singularities in the electrical variables [4][5]. To treat this new problem in the X-FEM, specific crack analysis tools and changes in the enrichment functions are needed which allows to represent the crack- both in the mechanical and electrical functional spaces. In this work, we will present these techniques and perform a convergence analysis to ensure that the crack tip behavior is accurately taken into account. Finally, we suggest a simple propagation model for crack growth