On a flexomagnetic behavior of composite structures

The popularity of the studies is getting further on the flexomagnetic (FM) response of nano-electro-magneto machines. In spite of this, there are a few incompatibilities with the available FM model. This study indicates that the accessible FM model is inappropriate when considering the converse magnetization effect that demonstrates the necessity and importance of deriving a new FM relation. Additionally, the literature has neglected the converse FM coefficient in the Lifshitz invariant inside the free energy constitutive relation. This fact inspires us to endeavor and conduct a new characteristic formulation for static analysis of axially compressed piezomagnetic nanobeams comprising the FM effect. This novel FM model is competent and suitable for various boundary conditions, encompassing analytical, semi-analytical, and numerical solving strategies. However, based on the previous FM equation established with respect to Euler-Bernoulli and Timoshenko beams, the governing equations are ill-posed due to the corresponding energy density. Despite that, this error will not remain in the finalized equations in the present model by conjecturing a gradient of the magnetic field and a different formulation. Moreover, the inverse FM parameter will appear in the magnetic field relation. As the literature reported, non-uniform deformed piezomagnetic structures are capable of presenting more outstanding flexomagneticity. In actuality, a non-uniform elastic strain appears as a response to the magnetic field gradient (converse effect) that causes this study to deduce the nanobeam with higher-order shear deformations. Furthermore, the local governing equations will be transferred into the nonlocal phase according to the nonlocal differential, particularly nonlocal integral elasticity which itself is a strong nonlocality. Through this theory, and in regard to the converse FM impact, an analytical expression is applied for computing critical buckling loads within several ends conditions of the nanobeam. Our present results and achievements will hopefully be an effective contribution to theoretical studies on the mechanics of intelligent nanostructures.