Finite deformation field near the tip of a Blatz–Ko wedge bonded to a rigid substrate
Finite deformation field near the tip of a Blatz–Ko wedge bonded to a rigid substrate
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粘合到刚性基底的 BlatzäKo 楔形尖端附近的有限变形场
DOI：
10.1007/s10704-022-00654-y
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发表时间：
2022
影响因子：
2.5
通讯作者：
Ciccotti, Matteo
中科院分区：
文献类型：
--
作者：
Hui, Chung-Yuen;Zhu, Bangguo;Ciccotti, Matteo
尖角或楔形在日常结构中很常见。根据楔体的内角不同，可能会出现严重的应力集中。线弹性理论预测，当一个不可压缩的弹性楔体粘结在刚性衬底上并受到平面应变变形时，楔体尖端的应力具有指数奇异性If。对于某些可压缩楔体，应力不仅是奇异的，而且会以无限快的速度振荡.在这里，我们表明，如果考虑大变形，这些结果不再成立。具体地，我们确定了Blatz-Ko楔形尖端附近的渐近场，并且发现应力场对没有幂奇异性。此外，应力场的指数奇异性不同于线弹性理论所预测的奇异性，不存在振荡现象。对于足够低的可压缩性，可以获得渐近级数的高阶项-类似于线性理论中的威廉展开。我们的渐近结果通过有限元计算得到了验证。我们还研究了90°楔形边界情况下的楔形尖端场。在这种情况下，应力奇异性至多是对数的。
Sharp corners or wedges are common in everyday structures. Depending on the internal angleof the wedge, severe stress concentration can occur. Linear elasticity predicts that when an incompressible elastic wedge is bonded to a rigid substrate and subjected to plane strain deformation, the stresses at the wedge tip has a power law singularity if. For someand for compressible wedges, the stresses are not only singular but oscillate infinitely rapidly. Here we show that these results are no longer true if large deformation is taken into consideration. Specifically, we determine the asymptotic fields near a tip of a Blatz–Ko wedge and found that the stress field has no power singularity for. Furthermore, the power law singularity of the stress field differs from those predicted by linear elasticity and there are no oscillations. For sufficiently low compressibility, it is possible to obtain higher order terms of the asymptotic series—analogous to William’s expansion in linear theory. Our asymptotic results are validated by finite element calculations. We also studied the wedge tip field for the borderline case of a 90° wedge. For this case, the stress singularity is found to be at most logarithmic.
不可压缩弹性材料有限平面应变裂纹尖端附近的平衡场
DOI：
--
发表时间：
1982
期刊：
影响因子：
--
作者：
R. A. Stephenson
通讯作者：
R. A. Stephenson
DOI：
10.1098/rsif.2013.0816
发表时间：
2014-02-06
期刊：
Journal of the Royal Society, Interface
影响因子：
--
作者：
Tramacere F;Kovalev A;Kleinteich T;Gorb SN;Mazzolai B
通讯作者：
Mazzolai B
DOI：
--
发表时间：
2013
影响因子：
11.1
作者：
S. Ornes
通讯作者：
S. Ornes