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This paperstudies a co m monly observed pheno menon:theinitiation offracturefro m cornersin a brittlesoft material. Arectangular hydrogelis prepared and glued bet weent wo plastic fil ms,such that the hydrogel meets the fil ms at 90◦ corners. When the t wo plastic fil ms are pulled, the hydrogel undergoes a shear defor mation, and the stress-strain curve is recorded until fracture initiatesfromacorner.WefindthattheshearmodulusisindependentofthethicknessHofthe hydrogel, but the shear strength scales as ~ H − 0.4. A nu merical si mulation sho ws a nonlinear elastic zone around the corner, in which the stress field varies slo wly. Ho wever, when the nonlinear elastic zone is s mall co mpared to the thickness, an annulus exists in which a singular fieldoflinearelasticityprevails.Inthisannulus,thestressfieldscales withthedistanceRfrom thecorneras ~R−0.41. Wecallthisconditionsmall-scalenonlinearelasticity. Ourresultsindicate thats mall-scale nonlinear elasticity prevails even whenthe appliedshearstrainis aslarge as 80 %. This condition explainsthe experi mentally observedscaling bet weenstrength andthickness. The c o n diti o n of s m all-s c al e n o nli n e ar el asti cit y si m pli fi es t h e c h ar a ct eri z ati o n of fr a ct ur e i niti at e d fro m corners of brittle soft materials.
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ELASTIC FIELDS AT CORNERS OF HIGHLY STRETCHABLE MATERIALS ARE CONCENTRATED BUT BOUNDED
ABSTRACT Corners concentrate elastic fields and often initiate fracture. For small deformations, it is well established that the elastic field around a corner is power-law singular. For large deformations, we show here that the elastic field around a corner is concentrated but bounded. We conduct computation and an experiment on the lap shear of a highly stretchable material. A rectangular sample was sandwiched between two rigid substrates, and the edges of the stretchable material met the substrates at 90° corners. The substrates were pulled to shear the sample. We computed the large-deformation elastic field by assuming several models of elasticity. The theory of elasticity has no length scale, and lap shear is characterized by a single length, the thickness of the sample. Consequently, the field in the sample was independent of any length once the spatial coordinates were normalized by the thickness. We then lap sheared samples of a polyacrylamide hydrogel of various thicknesses. For all samples, fracture initiated from corners, at a load independent of thickness. These experimental findings agree with the computational prediction that large-deformation elastic fields at corners are concentrated but bounded.
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- Award ID(s):
- 2011754
- PAR ID:
- 10500460
- Publisher / Repository:
- Rubber Chemistry and Technology
- Date Published:
- Journal Name:
- Rubber Chemistry and Technology
- Volume:
- 96
- Issue:
- 4
- ISSN:
- 0035-9475
- Page Range / eLocation ID:
- 478 to 488
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.5254/rct.2376991
