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Asymptotic Field Near the Tip of a Debonded Anticrack in an Anisotropic Elastic Material
The Quarterly Journal of Mechanics and Applied Mathematics ( IF 0.9 ) Pub Date : 2020-02-20 , DOI: 10.1093/qjmam/hbaa001
Xu Wang 1 , Peter Schiavone 2
Affiliation  

We use the sextic Stroh formalism to study the asymptotic elastic field near the tip of a debonded anticrack in a generally anisotropic elastic material under generalised plane strain deformations. The stresses near the tip of the debonded anticrack exhibit the oscillatory singularities |$r^{-3/4\pm i\varepsilon }$| and |$r^{-1/4\pm i\varepsilon }$| (where |$\varepsilon $| is the oscillatory index) as well as the real power-type singularities |$r^{-3/4}$| and |$r^{-1/4}$|⁠. Two complex-valued stress intensity factors and two real-valued stress intensity factors are introduced to respectively scale the two oscillatory and two real power-type singularities. The corresponding three-dimensional analytic vector function is derived explicitly, and the material force on the debonded anticrack is obtained. Our solution is illustrated using an example involving orthotropic materials.

中文翻译:

各向异性弹性材料中抗粘连裂纹尖端附近的渐近场

我们使用有性的Stroh形式主义来研究一般各向异性弹性材料在广义平面应变变形下脱粘抗裂尖端附近的渐近弹性场。|||||||||||| rr ^ {-3/4 \ pm i \ varepsilon} $ | | $ r ^ {-1/4 \ pm i \ varepsilon} $ | (其中| $ \ varepsilon $ |是振荡指数)以及实数幂型奇点| $ r ^ {-3/4} $ | | $ r ^ {-1/4} $ |⁠。引入两个复数值应力强度因子和两个实数值应力强度因子分别缩放两个振荡和两个实数幂型奇点。明确推导了相应的三维解析矢量函数,并获得了去粘防裂上的物质力。我们的解决方案使用涉及正交各向异性材料的示例进行了说明。
更新日期:2020-02-20
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