Explicit nonlinear homogenization for magneto-electro-elastic laminated materials

• We developed an homogenization scheme for nonlinear laminated materials.
• It is able to work with anisotropic magneto-electro-elastic components.
• It is based on an extension of the Backus–Tartar method.
• The procedure takes into account an arbitrary lamination direction.
• The explicit results can be easily implemented in a software code with standard operations of tensor calculus.

In this work we propose an explicit procedure for the homogenization of laminated magneto-electro-elastic nonlinear materials. It means that we determine the effective response of a multilayered structure composed of materials with an arbitrarily nonlinear and anisotropic coupled behavior. In order to obtain a general theory, we take into consideration an arbitrary lamination direction, which is useful to exploit the anisotropic character of components. This technique is characterized by closed form expressions, which can be simply implemented through the basic operations of tensor calculus. To conclude, we discuss some particular cases and various applications.