Spontaneous cavitation in growing elastic membranes

Joseph McMahon, Alain Goriely, Michael Tabor

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

One of the possible effects of volumetric growth in elastic materials is the creation of residual stresses. These stresses are known to change many of the classical properties of the material and have been studied extensively in the context of volumetric growth in biomechanics. Here we consider the problem of elastic cavitation in a growing compressible elastic membrane. Growth is taken to be homogeneous but anisotropic, and the membrane is assumed to remain axisymmetric during growth and deformation. We prove that neo-Hookean membranes cannot cavitate, but for Varga elastic materials we find conditions under which the material exhibits spontaneous cavitation in the absence of external loads, in marked distinction from the cavitation problem without growth.

Original languageEnglish (US)
Pages (from-to)57-77
Number of pages21
JournalMathematics and Mechanics of Solids
Volume15
Issue number1
DOIs
StatePublished - Jan 2010

Fingerprint

Cavitation
Membrane
Membranes
Elastic Material
Biomechanics
Residual Stress
Residual stresses

Keywords

  • Cavitation
  • Elasticity
  • Growth

ASJC Scopus subject areas

  • Materials Science(all)
  • Mathematics(all)
  • Mechanics of Materials

Cite this

Spontaneous cavitation in growing elastic membranes. / McMahon, Joseph; Goriely, Alain; Tabor, Michael.

In: Mathematics and Mechanics of Solids, Vol. 15, No. 1, 01.2010, p. 57-77.

Research output: Contribution to journalArticle

McMahon, Joseph ; Goriely, Alain ; Tabor, Michael. / Spontaneous cavitation in growing elastic membranes. In: Mathematics and Mechanics of Solids. 2010 ; Vol. 15, No. 1. pp. 57-77.
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