Mathematical solutions for moving generalized electric-magnetic-polarization saturation models in magneto-electro-elastic materials via weight functions

Abstract

This work presents an advanced analytical framework for solving moving generalized electric-magnetic-polarization saturation models in magneto-electro-elastic materials. The core methodology employs a weight function approach, which serves as a kernel to map applied electro-mechanical loads to stress intensity factors. The derivation involves solving boundary conditions using the crack opening displacement solution. A key contribution is the generalized strip yield model introduces a non-linear function $g\left(x\right)$ in the form $(g\left(x\right)D_s=\frac{\left|x^n\right|}{b^n}{D}_s)$. This allows flexibility in modeling saturation effects under varying displacement fields. Different $n-$ values correspond to different material responses, enabling the model to capture a range of non-linear behaviors. Validate the generalized strip yield model’s results by comparing them with solutions obtained via the stress function approach. Perform simulations to study crack-face boundary conditions under prescribed electro-mechanical loading. The results illustrate how SIFs vary with the size of the induction zone, saturation parameters, and the applied electro-mechanical fields. The agreement between the generalized model and direct analytical methods supports its accuracy.