Contact problems in multilayered piezoelectric media

An analytical methodology for the solution of frictionless contact problems for arbitrarily multilayered piezoelectric half-planes, when indented by a rigid rounded punch, is presented. The solution technique previously used to study the contact problems on elastic materials exhibiting real eigenvalues is further extended to accommodate both the presence of layers and half-planes composed of materials with electro-mechanical coupling and the presence of layers or half-planes with complex characteristic eigenvalues.; A generalized plane formulation is employed for the displacements u, v, w, and the electrostatic potential &phis; to obtain the equilibrium and the electrostatic charge equations. The solution to these governing equations is obtained by using the Fourier transform technique, along with the local/global stiffness matrix method. The local/global stiffness matrix approach involves reformulating the problem in the transform domain by expressing the interfacial tractions in terms of the interfacial displacements, thereby eliminating the Fourier coefficients. A local stiffness matrix in the transform domain is constructed for the type of layers and half-planes under consideration. This local stiffness matrix is then assembled into a global stiffness matrix for the entire multilayered half-plane by enforcing continuity conditions along the interfaces. Application of the mixed boundary conditions on the top surface of the half-plane indented by a rigid rounded punch results in a singular integral equation for the unknown pressure in the contact region.; The integral possesses a divergent kernel that is decomposed into Cauchy-type and regular parts using the asymptotic properties of the local/global stiffness matrices and the relationship existing between the Fourier and Hilbert transforms. This singular integral is numerically solved using a collocation technique based on the orthogonal properties of the Chebyshev polynomials first developed by Erdogan and Gupta. Numerical results are presented to illustrate the effect that the off-axis angle variation, stacking sequence, laminate configuration, and geometry have on the contact load versus contact length response, contact stress profile, and the magnitude of the electrostatic potential and normal electric displacement sensed by the piezoelectric layers.