Symplectic Contact Analysis of a Film-substrate System for High-throughput Material Characterization

Abstract

In this paper, the contact of a finite-sized film-substrate system is studied based on a symplectic approach. The horizontally graded film is the inhomogeneous sample adopted for high-throughput material characterization. The state equations with magneto-electro-elastic couplings are established in a dual form, with coefficient functions approximated by polynomials. Saint-Venant solutions and eigen-solutions of general eigenvalues are obtained and reformed analytically via symplectic orthogonality. After combining all the eigen-solutions, the coefficients in symplectic expansion are determined through Hamiltonian mixed energy variational principle. Generalized dual Hamiltonian transformation is introduced to derive analytical solutions. Theoretical results are validated and discussed through comparison with finite element analysis. A novel normal-tangential coupling phenomenon is observed and elucidated. The analytical framework herein serves as a robust theoretical foundation for subsequent advancement with respect to high-throughput material characterizations.

Keywords: symplectic approach, contact analysis, generalized dual Hamiltonian transformation, horizontally graded, material characterization, multi-field coupling