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首页> 外文期刊>Zeitschrift fur Angewandte Mathematik und Mechanik >Analytical solution for two equal collinear modified strip saturated cracks in 2-D semipermeable piezoelectric media
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Analytical solution for two equal collinear modified strip saturated cracks in 2-D semipermeable piezoelectric media

机译：2-D半透压电压介质中两个等相连改性条饱和裂缝的分析解

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摘要

An analytical solution and study is presented for two equal collinear cracks in 2-D semipermeable piezoelectric media based on modified strip saturation models. The constant saturated condition defined in strip saturation model is modified here by considering the symmetric and polynomial varying saturation conditions. These proposed saturated conditions are multiplicative of saturated electric displacement value and polynomial (constant to cubic order) of a variable defined as ratio of distance of a point on saturated zone length to the extended half-crack length. Moreover, these are interpolated on the basis of possible saturated values near the crack-tips and zone tips. To present the analytical study, a problem of two cracks of equal length situated in series is considered in 2-D arbitrary polarized infinite piezoelectric domain subjected to semipermeable crack-face and electromechanical loading conditions. Applying the extended Stroh formalism and complex variable approach, these problems are mathematically modeled into non-homogeneous Riemann Hilbert problems in terms of unknown complex functions representing stress and electric displacement components at any point within the domain. Using Muskhelishvili [1] and Collin's [2] mathematical techniques, these complex functions are obtained from the developed non-homogeneous Riemann Hilbert problems. Hence, the explicit expressions for saturated zone lengths (inner and outer), crack opening potentials (COPs), crack opening displacements (CODs) and local stress intensity factors (LSIFs) are obtained. Further, the impact of polynomial varying saturated conditions is highlighted on these fracture parameters with respect to inter crack space distance, crack-face conditions, polarization angle by presenting the numerical applications in infinite 2-D PZT-4 media.
机译：基于改进的条带饱和模型，在2-D半透电介质中的两个相等的共线裂缝提出了一种分析解决方案和研究。通过考虑对称和多项式不同的饱和度条件，在此处修改条带饱和度模型中定义的恒定饱和条件。这些所提出的饱和条件是多个变量的饱和电容值和多项式（常数为立方阶）的变量，该变量定义为饱和区长度对延伸的半裂纹长度的点的距离的距离。此外，这些基于裂缝提示和区域提示附近的可能的饱和值来插值。为了提出分析研究，在经过半透裂缝和机电负载条件的2-D任意偏振无限压电域中考虑了串联的相等长度的两个裂缝的问题。应用扩展的STROH形式和复杂的可变方法，这些问题在数学上建模到非同质的RIEMANN HILBERT问题中，而不是在域内的任何点表示应力和电置换分量的未知复杂功能。使用Muskhelishvili [1]和Collin的[2]数学技术，这些复​​杂的功能是从发发的非同质Riemann希尔伯特问题获得的。因此，获得了饱和区长度（内部和外部），裂缝开口电位（COP），裂缝开口位移（COD）和局部应力强度因子（LSIF）的显式表达式。此外，通过在无限的2-D PZT-4介质中呈现数值应用，在这些断裂参数上突出显示多项式变化饱和条件的影响。

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