Relation between crack surface displacements and strain energy release rate in thin rubber sheets

The classical problem of a small crack in the center of a large, thin rubber sheet deformed in simple tension, pure shear or equi-biaxial extension is revisited. Following Key (1969) and Lake (1970), the strain energy release rate for crack growth is derived by examining the crack surface displacements (crack opening) and considering the work that would be done by forces applied to close the crack again. It is shown that the strain energy release rate may be expressed in the same form for all three modes of deformation. The results have been verified using non-linear finite element analysis. Differences arising from the use of different hyper-elastic material models are discussed.

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