Axisymmetric contact and crack problems for an initially stressed neo-Hookean elastic layer

Dhaliwal, Ranjit S.; Singh, Brij Mohan; Rokne, Jon G.

doi:10.1016/0020-7225(80)90016-6

Cited by 25 publications

(4 citation statements)

References 14 publications

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“…A comparison between experiments carried out both in air and in water (Fig. (6)) show that the ρ s (λ) relationship is insensitive to such a change in adhesion. As stressed in the theoretical section, the isotropy condition for the displacements in the contact area is enforced by both adhesive and non-adhesive contacts.…”

Section: Resultsmentioning

confidence: 99%

Contact of a spherical probe with a stretched rubber substrate

Fretigny,

Chateauminois

2017

Preprint

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We report on a theoretical and experimental investigation of the normal contact of stretched neo-Hookean substrates with rigid spherical probes. Starting from a published formulation of surface Green's function for incremental displacements on a pre-stretched, neo-Hookean, substrate (L.H. Lee J. Mech. Phys. Sol. 56 (2008) 2957-2971), a model is derived for both adhesive and non-adhesive contacts. The shape of the elliptical contact area together with the contact load and the contact stiffness are predicted as a function of the in-plane stretch ratios λx and λy of the substrate. The validity of this model is assessed by contact experiments carried out using an uniaxally stretched silicone rubber. for stretch ratio below about 1.25, a good agreement is observed between theory and experiments. Above this threshold, some deviations from the theoretical prediction are induced as a result of the departure of the mechanical response of the silicone rubber from the neo-Hokeean description embedded in the model.

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Section: Resultsmentioning

confidence: 99%

Contact of a spherical probe with a stretched rubber substrate

Fretigny,

Chateauminois

2017

Preprint

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“…Woo and Shield [15] investigated the semi-infinite media in biaxial extension with a superposed force normal to the boundary. Equibiaxially stressed neo-Hookean half-space indented by a punch of arbitrary axisymmetric profile has been investigated by Dhaliwal et al [16] and for general hyperelastic (isotropic) bodies by Beatty and Usmani [17]. Karduna et al [18] performed finite element analysis of a Mooney-Rivlin type of rubber under equal-biaxial stretching and confirmed the theoretical predictions of Humphrey et al [19].…”

Section: Introductionmentioning

confidence: 80%

Evaluation of hyperelastic material properties based on instrumented indentation

Zafiropoulou¹,

Giannakopoulos²

2015

Surface and Contact Mechanics Including Tribology XII

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It is well known that instrumented indentation tests are useful tools in probing mechanical properties of materials such as metals and ceramics. Instrumented indentation of hyperelastic materials such as rubbers, bio-materials, tissues etc. has not been examined in depth, especially the inverse problem of material characterization from instrumented indentation response. The difficulty of the inverse problem for such materials is that the unknown property is a function, the elastic energy density function. There are several such functions and each function is often characterized by more than one parameter. If the maximum indentation depth is low, we have shown that instrumented indentation of initially unstretched hyperelastic materials can only resolve a combination of the material parameters. If the maximum indentation depth is high, the indentation can provide independent material properties, however not in a unique way. Moreover, high indentation loads could lead to surface puncturing and so blur the test results. In this work, we show that we can use spherical indentation of a substrate at different but known prestretch levels to obtain the involved material properties of the energy density function. The present methodology can also incorporate a limit energy failure criterion and instrumented indentation can incorporate this behavior which we may call indentation strength.

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“…The approaches [2,8] were used to analyze results on a number of problems in linearized solid mechanics: (i) contact interaction of elastic bodies with initial (residual) stresses [2, 6] and (ii) stability of local equilibrium of rock near mine workings [2] (these are problems for inhomogeneous subcritical states). There are also other reviews on linearized solid mechanics [4,5,7,[9][10][11][12][13][14][15]. The publications cited above are fully or partially related to the subject of the present paper: contact interaction of elastic punches and elastic bodies, both with initial (residual) stresses.…”

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confidence: 87%

Three-Dimensional Contact Problem for an Elastic Layer and a Cylindrical Punch with Prestresses

Ярецька

2014

Int Appl Mech

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An axisymmetric mixed problem for an elastic cylindrical punch pressed into a layer with initial (residual) stresses is solved using the linearized theory of elasticity. The analysis is performed in general form for the theory of large (finite) deformations and various theories of small initial deformations for an arbitrary elastic potential Keywords: linearized theory of elasticity, initial (residual) stresses, Fredholm equation, method of successive approximations Introduction. Results related to the three-dimensional linearized theory of stability of deformable bodies and the three-dimensional linearized theory of propagation of elastic waves in bodies with initial (residual) stresses are analyzed from a contemporary standpoint in [2,8]. The approaches [2,8] were used to analyze results on a number of problems in linearized solid mechanics: (i) contact interaction of elastic bodies with initial (residual) stresses [2, 6] and (ii) stability of local equilibrium of rock near mine workings [2] (these are problems for inhomogeneous subcritical states). There are also other reviews on linearized solid mechanics [4,5,7,[9][10][11][12][13][14][15]. The publications cited above are fully or partially related to the subject of the present paper: contact interaction of elastic punches and elastic bodies, both with initial (residual) stresses.The effect of a finite cylindrical punch on a half-space with initial (residual) stresses was analyzed in [3]. A general solution to the three-dimensional linearized axisymmetric problem for a rigid circular punch pressed without friction into a prestressed layer is presented in [1].In what follows, we will use the linearized theory of elasticity [2, 6] to solve a mixed axisymmetric problem for an elastic cylindrical punch pressed into a layer with initial (residual) stresses. Two cases will be examined: (i) a layer lies without friction on a rigid foundation and (ii) a layer is bonded to a rigid foundation. The analysis will be performed in general form for the theory of large (finite) initial deformations and various theories of small initial deformation for an arbitrary elastic potential.We will use the coordinates Oy i of the initial deformed configuration, which are related to the Lagrangian coordinates (natural configuration) by y i = l i x i ( , ) i = 1 3 , where l i are the elongations (the displacements of the initial configuration). Let the

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Axisymmetric contact and crack problems for an initially stressed neo-Hookean elastic layer

Cited by 25 publications

References 14 publications

Contact of a spherical probe with a stretched rubber substrate

Contact of a spherical probe with a stretched rubber substrate

Evaluation of hyperelastic material properties based on instrumented indentation

Three-Dimensional Contact Problem for an Elastic Layer and a Cylindrical Punch with Prestresses

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