Stretch-induced stress patterns and wrinkles in hyperelastic thin sheets

Nayyar, Vishal; Ravi‐Chandar, K.; Huang, Rui

doi:10.1016/j.ijsolstr.2011.09.004

Cited by 122 publications

(113 citation statements)

References 34 publications

(48 reference statements)

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“…The compiled system of nonlinear algebraic equations are the discretized Euler-Lagrange equations associated with eq. (20).…”

Section: A Model Of Thin Orthotropic Plates Under Finite In-plane Strmentioning

confidence: 99%

“…50% stretch). Papers in the literature tend to present pure numerical simulations [6,22,20,5,27]; experimental works either aim to incorporate plastic response [30,21] or compare results measured on elastomers against numerical data based on linear elasticity [19]. In accordance with the general expectation, the stretch needed for well developed wrinkled patterns (approx.…”

Section: Introductionmentioning

confidence: 99%

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Disappearance of stretch-induced wrinkles of thin sheets: A study of orthotropic films

Sipos

Fehér

2016

International Journal of Solids and Structures

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Abstract. A recent paper (Healey et al., J. Nonlin. Sci., 2013, 23, 777-805.) predicted the disappearance of the stretch-induced wrinkled pattern of thin, clamped, elastic sheets by numerical simulation of the Föppl-von Kármán equations extended to the finite in-plane strain regime. It has also been revealed that for some aspect ratios of the rectangular domain wrinkles do not occur at all regardless of the applied extension. To verify these predictions we carried out experiments on thin (20 µm thick adhesive covered), previously prestressed elastomer sheets with different aspect ratios under displacement controlled pull tests. On one hand the the adjustment of the material properties during prestressing is highly advantageous as in targeted strain regime the film becomes substantially linearly elastic (which is far not the case without prestress). On the other hand a significant, non-ignorable orthotropy develops during this first extension. To enable quantitative comparisons we abandoned the assumption about material isotropy inherent in the original model and derived the governing equations for an orthotropic medium. In this way we found good agreement between numerical simulations and experimental data.Analysis of the negativity of the second Piola-Kirchhoff stress tensor revealed that the critical stretch for a bifurcation point at which the wrinkles disappear must be finite for any aspect ratio. On the contrary there is no such a bound for the aspect ratio as a bifurcation parameter. Physically this manifests as complicated wrinkled patterns with more than one highly wrinkled zones on the surface in case of elongated rectangles. These arrangements have been found both numerically and experimentally. These findings also support the new, finite strain model, since the Föppl-von Kármán equations based on infinitesimal strains do not exhibit such a behavior.

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“…The compiled system of nonlinear algebraic equations are the discretized Euler-Lagrange equations associated with eq. (20).…”

Section: A Model Of Thin Orthotropic Plates Under Finite In-plane Strmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Disappearance of stretch-induced wrinkles of thin sheets: A study of orthotropic films

Sipos

Fehér

2016

International Journal of Solids and Structures

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“…Wrinkles are commonly observed in natural materials [19,20], on stretched membranes and thin films [21][22][23][24][25][26][27][28], in synthetic materials [28,29], on surface growth of oxides [30] and on the solidified surface of liquid [31]. They typically account for applied strains or stress relaxations in the thin materials.…”

Section: Microstructures Of Wedged and Cylindrical Ingots Of Fe 50 Nimentioning

confidence: 99%

“…, with, L and t respectively the length after stretching and the thickness of the membrane and ε the strain, ε = L − Lo/Lo, Lo initial length [23] for strained membrane or as λ/t = 2πK 1/3 [24], with K = E s /4E m (1 − πν s 2 ); E s and E m , respectively Young modulus of the substrate and the membrane, ν s the Poisson ratio of the substrate for strain relaxation of the membrane. The wrinkles on the surface of the BMG can be then undoubtedly interpreted as the formation of strained layered thin film as part of the aggregates bulk.…”

Section: Microstructures Of Wedged and Cylindrical Ingots Of Fe 50 Nimentioning

confidence: 99%

Development of Fe-B Based Bulk Metallic Glasses: Morphology of Residual Phases in Fe50Ni16Mo6B18Zr10 Glass

Aboki

2013

Metals

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Iron-boron based bulk metallic glasses (BMG) development has been initiated using Fe 40 Ni 38 Mo 4 B 18 as precursor. Addition of zirconium up to 10 atomic % along with the reduction of Ni proportion improves the glass forming ability (GFA), which is optimum when Ni is suppressed in the alloy. However melting instability occurred during the materials fabrication resulting in the formation of residual crystalline phases closely related to the amorphous phase. Microstructure study shows an evolution from amorphous structure to peculiar acicular structure, particularly for Fe 50 Ni 16 Mo 6 B 18 Zr 10 , suggesting the amorphous structure as interconnected atomic sheets like "atomic mille feuilles" whose growth affects the alloys' GFA.

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“…Pre-wrinkled conductive films have been used in micro-scaled modern technology in large-area electronics, capacitors, and polymer actuators, 7,8 and in medical surgery involved in treating wrinkling skin cases. 9 In addition to skin aging and wound healing, thin film wrinkling can be found in other fields such as semiconductor technology, 10 sandwich structure failure as face wrinkling, 11 stretchable connectors, 12 topographic matrices for cell alignment in bioengineering, metrology of material properties, 13,14 stretched thin sheets, [15][16][17][18][19] sheet metal forming and patterning, and topographical surface structuring. [20][21][22][23] From the numerous literature survey some related references are illustrated for example.…”

Section: Introductionmentioning

confidence: 99%

Wrinkling of extensional thin films through modified large deflection equations analytically and experimentally

Jen

2015

AIP Advances

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The stretch-induced wrinkling of thin films is solved through the modified von Kármán large deflection equations by first selecting the suitable deformation expressions that satisfy boundary conditions. Then, adopting the principle of minimum potential energy we obtain the deformations of simply supported rectangular thin films. The obtained significant deflections are nonlinearly elastic and of the lowest order of infinite solutions. The parameters of aspect ratio, the thickness and material of thin films are studied analytically and numerically. The highlighted results of wrinkle amplitude and load are in good agreement with experiments. The methodology also indicates the limit load impending plasticity and predicts the applied load precisely for each wrinkle. Further, it can be extended to the variety of multifunctional orthotropic and multi-layered thin films.

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Stretch-induced stress patterns and wrinkles in hyperelastic thin sheets

Cited by 122 publications

References 34 publications

Disappearance of stretch-induced wrinkles of thin sheets: A study of orthotropic films

Disappearance of stretch-induced wrinkles of thin sheets: A study of orthotropic films

Development of Fe-B Based Bulk Metallic Glasses: Morphology of Residual Phases in Fe50Ni16Mo6B18Zr10 Glass

Wrinkling of extensional thin films through modified large deflection equations analytically and experimentally

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