A consistent framework of material configurational mechanics in piezoelectric materials

Abstract

The fundamental concepts of material configurational mechanics are formulated in piezoelectric materials. A consistent thermodynamic framework is outlined to develop the corresponding theory of material configurational stresses and forces associated with the \(J_{k}\)-, M- and L-integrals by the gradient, divergence and curl operation of the electric enthalpy density, respectively. The physical interpretation of material configurational stresses is explored, and they can be explained as the energy release rates due to the translation of material point along \(x_{k}\)-direction, the self-similar expansion, the rotation of material element, respectively. The path independence or path dependence of variant integrals such as the \(J_{k}\)-, M- and L-integrals is examined in piezoelectric material. As an application of material configurational mechanics in piezoelectric materials, an explicit method is derived to calculate the change of the J-integral as a dominant fracture parameter for a crack interaction with domain switching near the crack tip. It is concluded that domain switching has an obvious shielding effect on the fracture toughness in piezoelectrics by the present explicit forms. The present framework of material configurational mechanics is expected to provide an effective and convenient tool to deal with various crack or damage problems in piezoelectric materials.