On the cavitation of a swollen compressible sphere in finite elasticity

Pence, Thomas J.; Tsai, Hungyu

doi:10.1016/j.ijnonlinmec.2004.06.004

Cited by 16 publications

(24 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The foregoing argument about the decay of energy is thus applicable to π with the load potential equal to a constant. This is the free-swelling problem, and plays a central role in [Treloar 1975;Pence and Tsai 2005;Hong et al 2008;Duda et al 2010;Chester and Anand 2011], where it is used to specify constitutive information; i.e., restrictions on the response of the gel at points in κ.…”

Section: Appendix A: Proof Of Theoremmentioning

confidence: 99%

“…(a) In the first, which is tacitly adopted in [Pence and Tsai 2005;Chester and Anand 2011], the flux m · n is unrestricted on ∂π; this requires µ to vanish there, and the local inequality (56) is satisfied if d(π ) → 0, withċ unrestricted. This in turn requires that µ = 0 pointwise, ensuring that the condition on the boundary is satisfied.…”

Section: Appendix A: Proof Of Theoremmentioning

confidence: 99%

“…In fact we are able to weaken this requirement to rank-one convexity. Accordingly the decomposition of the deformation into elastic and swelling deformations, assumed a priori in current theories of diffusion in polymers [Pence and Tsai 2005;Hong et al 2008;Duda et al 2010;Chester and Anand 2011;Duda et al 2011], is meaningful for free-energy functions commonly used to model elastomers. Moreover, because of the basic role played by polyconvexity in Ball's landmark existence theory [1977] for conventional elasticity, our results indicate that an extension of that theory to accommodate diffusion should be feasible.…”

Section: Introductionmentioning

confidence: 99%

“…We may also use the swelling constraint to eliminate the concentration in favor of i 3 and thus express the energy as a function of {i 1 , i 2 , i 3 }, in the manner of a conventional compressible solid [Treloar 1975;Pence and Tsai 2005;Pence and Tsai 2006;Deng and Pence 2010], albeit subject to the requirement i 3 > 1. In this interpretation we write (31) in the form…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Untitled

2013

Math. Mech. Compl. Sys.

View full text Add to dashboard Cite

We derive the detailed structures of the 6 × 6 matrices N i and N (−1) i (i = 1, 2, 3) in the Stroh formalism of anisotropic elasticity for quasicrystals. All six matrices are expressed explicitly in terms of the sixty-six reduced elastic compliances. The Green's functions for bi-quasicrystals are also obtained. Next, we derive compliant and stiff interface models in anisotropic quasicrystalline bimaterials. It is observed that the phonon normal traction is always continuous across the stiff interface. Finally we present the asymptotic fields associated with a tractionfree, semi-infinite interface crack in anisotropic quasicrystalline bimaterials and solve the collinear interface crack problem. The interface crack-tip field consists of three two-dimensional oscillatory singularities which are evaluated via the introduction of three complex stress intensity factors.

show abstract

Section: Appendix A: Proof Of Theoremmentioning

confidence: 99%

Section: Appendix A: Proof Of Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Untitled

2013

Math. Mech. Compl. Sys.

View full text Add to dashboard Cite

show abstract

“…More closely related to the current study is the growing interest in cavitation in soft and biological materials. For example, David and Humphrey [34] studied the stress and strain concentration due to the introduction of a circular hole in an anisotropic bio-tissue, Merodio and Saccomandi [35] studied the effect of fibre-reinforcement in the radial direction, McMahon et al [36] and Pence and Tsai [37][38] investigated cavitation due to growth and swelling, respectively, and Volokh [39] suggested that cavitation instability could be a rational indicator of aneurysm rupture.…”

Section: Introductionmentioning

confidence: 99%

On the near-critical behavior of cavitation in elastic plane membranes

Geng

Cai

2017

International Journal of Non-Linear Mechanics

View full text Add to dashboard Cite

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. AbstractMaterial cavitation under tensile loading is often studied by assuming the pre-existence of a small void. In this case the void would initially grow but without significant change in its size, and cavitation is said to take place if this slow growth is followed by rapid growth at higher load values. In the limit when the original void radius δ tends to zero, there will be no growth until a load or stretch measure, λ say, reaches a well-defined critical value λ cr at which a cavity appears suddenly. In this paper we study the near-critical asymptotic behavior of cavitation in plane membranes when δ is not zero but small, and show that the near-critical behavior is governed by a scaling law in the form λ − λ cr = C(δ/L) m , where L is the undeformed outer radius of the plane membrane, and C and m are non-dimensional constants. The positive power m in general depends on the material model used, but for the three classes of material models considered, it happens to be equal to 2(1 + ν)/(3 + ν) in each case, where ν is Poisson's ratio for infinitesimal deformations. If a pre-existing void is viewed as an imperfection, then this scaling law describes the imperfection sensitivity of cavitation: it states that in the presence of imperfections significant void growth would occur when λ were increased to within an order (δ/L) m interval around λ cr .

show abstract