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.

中文翻译：

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基于梯度理论的磁电弹性固体裂纹分析

摘要 本文提出了一种计算方法来分析由梯度理论描述的磁电弹性固体中二维裂纹问题和直接挠曲电效应。针对这些问题开发了有限元方法 (FEM)，其中电位移和磁感应的本构方程包含应变梯度。保持在这些项上的系数与缩放参数成正比。它表达了所考虑的高级连续模型中的尺寸效应现象。控制方程是通过应用变分原理推导出来的。随后为磁电弹性梯度理论开发和实施 FEM 公式。路径无关的 J 积分是在所考虑的理论框架中导出的。