The delamination of a growing elastic sheet with adhesion

Napoli, Gaetano; Turzi, Stefano

doi:10.1007/s11012-017-0618-0

Cited by 15 publications

(18 citation statements)

References 17 publications

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“…Thus, from here on, we refer to the first blister solution as the one that is physically accessible. We note that this subtle, nonmonotonic behavior of the pressure-displacement relation has already been observed in other closely related systems [34,58,59].…”

Section: A Energy and Pressure-displacement Relationsupporting

confidence: 78%

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Delamination of a thin sheet from a soft adhesive Winkler substrate

et al. 2018

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A uniaxially compressed thin elastic sheet that is resting on a soft adhesive substrate can form a blister, which is a small delaminated region, if the adhesion energy is sufficiently weak. To analyze the equilibrium behavior of this system, we model the substrate as a Winkler or fluid foundation. We develop a complete set of equations for the profile of the sheet at different applied pressures. We show that at the edge of delamination, the height of the sheet is equal to sqrt[2]ℓ_{c}, where ℓ_{c} is the capillary length. We then derive an approximate solution to these equations and utilize them for two applications. First, we determine the phase diagram of the system by analyzing possible transitions from the flat and wrinkled to delaminated states of the sheet. Second, we show that our solution for a blister on a soft foundation converges to the known solution for a blister on a rigid substrate that assumed a discontinuous bending moment at the blister edges. This continuous convergence into a discontinuous state marks the formation of a boundary layer around the point of delamination. The width of this layer relative to the extent length of the blister, ℓ, scales as w/ℓ∼(ℓ_{c}/ℓ_{ec})^{1/2}, where ℓ_{ec} is the elastocapillary length scale. Notably, our findings can provide guidelines for utilizing compression to remove thin biofilms from surfaces and thereby prevent the fouling of the system.

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Section: A Energy and Pressure-displacement Relationsupporting

confidence: 78%

“…In addition, the latter systems evolve into a state of multiple blisters and as explained in Ref. [58], this state is energetically unfavorable in the present model.…”

Section: Formation Of a Boundary Layer At The Edge Of A Large Blistersupporting

confidence: 51%

Delamination of a thin sheet from a soft adhesive Winkler substrate

et al. 2018

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“…Von Kármán theory is adapted in [30] to describe the evolution of films already debonded from a substratum forming blisters. [31] characterizes the onset of delamination in films whose edges are kept fixed while growing attached to a substrate. A situation closer to the geometry under study here is considered in [10] by means of a neo-Hookean elastic energy.…”

Section: Von Kármán Approximation For the Agar/biofilm Interfacementioning

confidence: 99%

Biofilms as poroelastic materials

Carpio

Cebrián

Vidal

2019

International Journal of Non-Linear Mechanics

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Biofilms are bacterial aggregates encased in a self-produced polymeric matrix which attach to moist surfaces and are extremely resistant to chemicals and antibiotics. Recent experiments show that their structure is defined by the interplay of elastic deformations and liquid transport within the biofilm, in response to the cellular activity and the interaction with the surrounding environment. We propose a poroelastic model for elastic deformation and liquid transport in three dimensional biofilms spreading on agar surfaces. The motion of the boundaries can be described by the combined use of Von Kármán type approximations for the agar/biofilm interface and thin film approximations for the biofilm/air interface. Bacterial activity informs the macroscopic continuous model through source terms and residual stresses, either phenomenological or derived from microscopic models. We present a procedure to estimate the structure of such residual stresses, based on a simple cellular automata description of bacterial activity. Inspired by image processing, we show that a filtering strategy effectively smooths out the rough tensors provided by the stochastic cellular automata rules, allowing us to insert them in the macroscopic model without numerical instability.

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“…The topic of fracture in soft materials is the focus of the papers [14,15]. Napoli and Turzi examine the delamination and buckling of a growing elastic sheet subject to capillary adhesion [14].…”

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confidence: 99%

“…Napoli and Turzi examine the delamination and buckling of a growing elastic sheet subject to capillary adhesion [14]. Lucantonio and Noselli analyze the impact of rate-dependent factors on the toughness of poroelastic composites [15].…”

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confidence: 99%