Crack analysis in magneto-electro-elastic solids by gradient theory

Abstract

This paper presents a computational method to analyze 2D crack problems in magneto-electro-elastic solid described by the gradient theory with the direct flexoelectric effect. The finite-element method (FEM) is developed for these problems, where the constitutive equations for electric displacement and magnetic induction contain the strain-gradients. The coefficients staying at these terms are proportional to the scaling parameters. It expresses the size effect phenomenon in the considered advanced continuum model. The governing equations are derived by applying the variational principle. The FEM formulation is subsequently developed and implemented for the gradient theory of magneto-electro-elasticity. The path-independent J-integral is derived in the framework of considered theory.

Keywords:

• Finite-element method
• size effect
• flexoelectricity
• in-plane crack problems
• J-integral

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Slovak Science and Technology Assistance Agency [grant number APVV-14-0216], [grant number VEGA 1/0145/17] and the Slovak Academy of Sciences Project (SASPRO) [grant number 0106/01/01].