Dual Hamiltonian transformation and magneto-electro-thermo-viscoelastic contact analysis

Abstract

The application of high-throughput testing methodologies and the involvement of functionally graded specimens for material characterization show immense potential and plays an indispensable role in the progressive advent of advanced materials. Nevertheless, the inherent material inhomogeneity and multi-field coupling pose great obstacles in the fundamental theory and analysis for the behavior of functionally graded specimens, thus necessitating the proposal of new and innovative analytical approaches. Here, the contact model and analysis of a finite-sized magneto-electro-thermo-viscoelastic plane with a horizontal exponential material gradient is established based on a new symplectic approach. With prior linearization via Laplace transform, the state equations are constructed in the matrix form, resulting in the dual Hamiltonian transformation under homogeneous displacement constraint. The dual adjoint symplectic orthogonality is introduced and proved, elucidating the implications of symmetry breaking. General and particular solutions are derived to constitute the complete solution in the symplectic expansion. The analytical solution is verified by comparing with highly precise finite element solutions in the entire domain. This current work not only paves the way for an efficient and robust analytical framework via the symplectic methodology, but also sets a foundation with benchmark exact solutions for future research endeavors.