Hamiltonian Approach to Piezoelectric Fracture

The electroelastic behavior of a piezoelectric multi-material with a V-notch is investigated in this study, via a Hamiltonian approach. At first, we consider the piezoelectric field of the structure, by extending ZHONG's formalism [1] to linear piezoelectricity, through the Two Extreme Point's problem. Following a unified description of ZHONG and BUI's formalisms [2], we present a formulation of electro elastic fields at the notch tip, through the canonical equations of Hamilton. A piezoelectric multi-material problem is thus reduced to a single-material problem, with a relative simplification of the constitutive equations in the form of a first-order ordinary differential system, from which derives an original method for determining the singularity degree for two-dimensional piezoelectric structures with a V-notch.The procedure is then applied to a bi-material piezoelectric specimen in order to determine the stress amplitude and the singularity degree close to the notch tip as function of the electric field and the notch angle.