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"This paper studies the lap shear, in which both the adhesive and adherends are elastic, but the adhesive is much softer than the adherends. The shear lag model identifies a length, called the shear lag length Ls. The energy release rate of a debond crack is affected by the elasticity of both the adhesive and adherends. Their relative importance is characterized by the ratio of the length of the remaining joint, L, to the shear lag length, Ls. In the short-joint limit, L/Ls→0, the adherends do not deform, and the elasticity of the adhesive gives the energy release rate. In the long-joint limit, L/Ls→∞, the interior of the adhesive does not deform, and the elasticity of the adherends gives the energy release rate. The shear lag model gives an approximate expression of the energy release rate for all values of L/Ls. This expression is in excellent agreement with the results obtained by finite element calculations, so long as the crack is long compared to the thickness of the adhesive."
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Global existence for the two-dimensional Kuramoto–Sivashinsky equation with a shear flow
Abstract We consider the Kuramoto–Sivashinsky equation (KSE) on the two-dimensional torus in the presence of advection by a given background shear flow. Under the assumption that the shear has a finite number of critical points and there are linearly growing modes only in the direction of the shear, we prove global existence of solutions with data in $$L^2$$ L 2 , using a bootstrap argument. The initial data can be taken arbitrarily large.
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- PAR ID:
- 10338800
- Date Published:
- Journal Name:
- Journal of Evolution Equations
- Volume:
- 21
- Issue:
- 4
- ISSN:
- 1424-3199
- Page Range / eLocation ID:
- 5079 to 5099
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript
- Journal Article:
- https://doi.org/10.1007/s00028-021-00752-9
