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首页> 外文期刊>Composite Structures >Investigation of anti-plane shear behavior of a Griffith permeable crack in functionally graded piezoelectric materials by use of the non-local theory
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Investigation of anti-plane shear behavior of a Griffith permeable crack in functionally graded piezoelectric materials by use of the non-local theory

机译：利用非局部理论研究功能梯度压电材料中格里菲斯可渗透裂纹的反平面剪切行为

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In this paper, the non-local theory of elasticity is applied to obtain the behavior of a Griffith crack in functionally graded piezoelectric materials under the anti-plane shear loading for the permeable electric boundary conditions. To make the analysis tractable, it is assumed that the material properties vary exponentially with coordinate vertical to the crack. By means of the Fourier transform, the problem can be solved with the help of a pair of dual-integral equations that the unknown variable is the jump of the displacement across the crack surfaces. These equations are solved by use of the Schmidt method. Numerical examples are provided. Unlike the classical elasticity solutions, it is found that no stress and electric displacement singularities are present near the crack tips. The non-local elastic solutions yield a finite hoop stress at the crack tips, thus allows us to using the maximum stress as a fracture criterion. The finite hoop stresses at the crack tips depend on the crack length, the functionally graded parameter and the lattice parameter of the materials, respectively.
机译：本文采用非局部弹性理论来获得功能性梯度压电材料在可渗透电边界条件下的反平面剪切载荷下的格里菲斯裂纹行为。为了使分析更容易进行，假设材料属性与垂直于裂纹的坐标呈指数变化。通过傅立叶变换，可以借助一对双重积分方程来解决该问题：未知变量是位移在裂纹表面上的跳跃。这些方程式通过使用Schmidt方法求解。提供了数值示例。与经典的弹性解不同，发现裂纹尖端附近没有应力和电位移奇异点。非局部弹性解在裂纹尖端产生有限的环向应力，因此允许我们将最大应力用作断裂准则。裂纹尖端的有限环向应力分别取决于材料的裂纹长度，功能梯度参数和晶格参数。

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