Symplectic contact analysis of a finite-sized horizontally graded magneto-electro-elastic plane

Material characterization using high-throughput testing (HTT) techniques has shown great promise in expediting the advancement of high-performance materials. A key step in HTT is the adoption of functionally graded specimens, whose material inhomogeneity, however, imposes a great challenge for analytically evaluating its responsive behaviour under external loads. This work establishes the first symplectic framework for contact analysis of a finite-sized magneto-electro-elastic plane with an exponential material gradient along the horizontal direction. The governing equations are first represented in matrix form in a state space, with the full state vector defined and the operator matrix derived. The operator matrix is found to be distinct from the Hamiltonian operator matrix in the case of a homogeneous medium. With all the eigen-solutions obtained, the Hamiltonian mixed energy variational principle is then introduced to derive the coefficients in the symplectic expansion. The developed analytical solution not only exhibits asymmetry properties but also converges rapidly. The analytical results are validated through comparison with the finite element simulations. The analytical platform established here would work as an effective theoretical basis for the subsequent development of quantitative HTT techniques.