Refined layer-wise models for nonlocal analysis of magneto-electro-elastic plates

Size-dependent theories of continuum mechanics are an important tool for structural and material modeling in engineering applications, with particular regard to those involving micro- and nano-scales. Among various approaches proposed in the literature to account for the effect of the microstructure via continuum models, the Eringen’s nonlocal elasticity model incorporates important features of material behavior via a differential stress-strain relationship involving a scale coefficient, or characteristic length, depending on the material microstructure [1]. In the framework of Eringen’s nonlocal elasticity, plate theories have been reformulated for homogeneous and multilayered configurations also extending the models to multifield problems. The literature review reveals that the proposed two-dimensional models for multilayered plates are based on the equivalent single layer with some limitations. Indeed, the equivalent single layer models do not allow to accurately capture the through-the-thickness distribution of the unknown fields. Additionally, in the nonlocal material behavior framework, the proposed equivalent single layer theories account for a unique value of the characteristic length common to all of the layers, whereas this parameter can exhibit meaningful variability for layers of different materials. Here, nonlocal layer-wise plate theories for the analysis of magneto-electro-elastic multilayered plates are presented. They are obtained assuming Eringen’s nonlocal behavior for the layers. The plate governing equations are obtained via the Reissner’s mixed variational theorem (RMVT), assuming the generalized displacements and generalized out-of-plane stresses as primary variables. These are expressed as through-the-thickness expansions of suitably selected functions, considering the expansion order as a formulation parameter [2]. Different advanced high order nonlocal plate theories are then generated using a layer-based assembly algorithm of the so-called fundamental nuclei associated with the variable expansion terms. The use of the LW approach and RMVT allows for (i) the explicit fulfillment of the transverse generalized stress interface equilibrium, which is crucial for a correct description of the plate fields, (ii) the straightforward analysis of plates with layers exhibiting different nonlocality characteristic lengths. To illustrate the features of the proposed nonlocal plate theories Navier solution results are presented and discussed. Additionally, finite elements are developed basing on the proposed theories and their performances discussed. References [1] A. Eringen, Nonlocal Continuum Field Theories, Berlin: Springer, 2002. [2] E. Carrera, Developments, ideas, and evaluations based upon Reissner’s mixed variational theorem in the modeling of multilayered plates and shells, Applied Mechanics Review, vol. 54, no. 4, pp.301–328, 2001.