A size-dependent elastic theory for magneto-electro-elastic materials

A size-dependent elastic theory for magneto-electro-elastic (MEE) nano-materials is proposed. The theory features not only the inclusion of the classical parameters such as piezoelectric and piezomagnetic constants, the magneto-electro, dielectric and magnetic permeability coefficients, but also the nonlocal and strain gradient parameters and their induced high-order MEE parameters. The governing equations and the boundary conditions are derived with the aid of the variational principle. To illustrate the theory, the general solutions of the complete boundary value problems of a one-dimensional beam problem is formulated. It is found that the equation of motion of the present beam model is two orders higher than that of the classical Euler—Bernoulli model. Therefore, it indicates that the general solutions presented in this paper may be served as benchmark theoretical results for the future study. •Conventional MEE parameters are size-dependence.•Formulation of the boundary value problems for MEE materials.•General solutions and specific solutions for one-dimensional beam models.