A simplified formulation of adhesion problems with elastic plates

Majidi, Carmel; Adams, George G.

doi:10.1098/rspa.2009.0060

Cited by 39 publications

(36 citation statements)

References 15 publications

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“…In the preceding section, we derived results for two partial constraint problems for an elastica using singular balances of force, moment, and energy (3)- (5), and some additional kinematic information. In the present section, we discuss an alternate framework in which a singular balance of material force (6) is used in lieu of the energy balance (5). O'Reilly proposed such a balance law for rods [34], compared it with the energy balance law [36], and employed it in a number of settings including that of Bigoni's sleeve problems [25,29].…”

Section: Comparison With Materials Force Balancementioning

confidence: 99%

Partial Constraint Singularities in Elastic Rods

Hanna

Singh

Virga

2018

J Elast

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We present a unified classical treatment of partially constrained elastic rods. Partial constraints often entail singularities in both shapes and reactions. Our approach encompasses both sleeve and adhesion problems, and provides simple and unambiguous derivations of counterintuitive results in the literature. Relationships between reaction forces and moments, geometry, and adhesion energies follow from the balance of energy during quasistatic motion. We also relate our approach to the balance of material momentum and the concept of a driving traction. The theory is generalizable and can be applied to a wide array of contact, adhesion, gripping, and locomotion problems.

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Section: Comparison With Materials Force Balancementioning

confidence: 99%

Partial Constraint Singularities in Elastic Rods

Hanna

Singh

Virga

2018

J Elast

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“…The latter comes from the condition associated with perturbations δq α . The equations (27) are the Donnell equations for thin cylindrical shells, see for instance [23]. The first equation (27a) is a tangential balance of forces.…”

Section: Equations Of Equilibriummentioning

confidence: 99%

Capillary buckling of a thin film adhering to a sphere

Hure

Audoly

2013

Journal of the Mechanics and Physics of Solids

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We present a combined theoretical and experimental study of the buckling of a thin film wrapped around a sphere under the action of capillary forces. A rigid sphere is coated with a wetting liquid, and then wrapped by a thin film into an initially cylindrical shape. The equilibrium of this cylindrical shape is governed by the antagonistic effects of elasticity and capillarity: elasticity tends to keep the film developable while capillarity tends to curve it in both directions so as to maximize the area of contact with the sphere. In the experiments, the contact area between the film and the sphere has cylindrical symmetry when the sphere radius is small, but destabilises to a non-symmetric, wrinkled configuration when the radius is larger than a critical value. We combine the Donnell equations for near-cylindrical shells to include a unilateral constraint with the impenetrable sphere, and the capillary forces acting along a moving edge. A non-linear solution describing the axisymmetric configuration of the film is derived. A linear stability analysis is then presented, which successfully captures the wrinkling instability, the symmetry of the unstable mode, the instability threshold and the critical wavelength. The motion of the free boundary at the edge of the region of contact, which has an effect on the instability, is treated without any approximation

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“…This moment-discontinuity method from Pamp and Adams [7] and Majidi and Adams [16,17] gives which when applied to Eq. (1) leads to Ay (4) (5) Interestingly the force, F, for this model is a constant value of 47tx/2DAy which is independent of ä, and only dependent on the flexural rigidity and the work of adhesion.…”

Section: Smail Deflection Theorymentioning

confidence: 84%

“…1). The recently developed moment-discontinuity method [3,16,17], is used to relate the work of adhesion to the discontinuity in the internal bending moment at the contact boundary, which is then used to find the radius of contact. This method greatly simplifies the analysis as it eliminates the explicit need to calculate and then minimize the total potential energy.…”

Section: Introductionmentioning

confidence: 99%

A Model of a Trapped Particle Under a Plate Adhering to a Rigid Surface

Parent¹,

Adams

2013

Journal of Applied Mechanics

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A Model of a Trapped Particle Under a Plate Adhering to a Rigid SurfaceMicro and nanomechanics are growing fields in the semiconductor and related industries. Consequently obstacles, such as particles trapped between layers, are becoming more important and warrant further attention. In this paper a numerical solution to the von Kármán equations for moderately large deflection is used to model a plate deformed due to a trapped particle lying between it and a rigid substrate. Due to the small scales involved, the effect of adhesion is included. The recently developed moment-discontinuity method is used to relate the work of adhesion to the contact radius without the explicit need to calculate the total potential energy. Three different boundary conditions are considered-the full clamp, the partial clamp, and the compliant clamp. Curve-fit equations are found for the numerical solution to the nondimensional coupled nonlinear differential equations for moderately large deflection of an axisymmetric plate. These results are found to match the small deflection theory when the deflection is less than the plate thickness. When the maximum deflection is much greater than the plate thickness, these results represent the membrane theory for which an approximate analytic solution exists.

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A simplified formulation of adhesion problems with elastic plates

Cited by 39 publications

References 15 publications

Partial Constraint Singularities in Elastic Rods

Partial Constraint Singularities in Elastic Rods

Capillary buckling of a thin film adhering to a sphere

A Model of a Trapped Particle Under a Plate Adhering to a Rigid Surface

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