Large deformations near a tip of an interface-crack between two Neo-Hookean sheets

Abstract

This paper contains an asymptotic investigation -within the nonlinear theory of elastostatic plane stress -of the deformations and stresses near the tips of a traction-free interface-crack between two dissimilar semi-infinite Neo-Hookean sheets. The results obtained are free of oscillatory singularities of the kind predicted by the linearized theory, which would require the two deformed faces of an interface-crack to overlap in the vicinity of its tips. Instead, the crack is found to open smoothly near its ends, regardless of the specific loading at infinity.

Finite deformation crack-line fields in a thin elasto-plastic sheet

“…Kirchhoff stress does not vary significantly throughout the thickness, and that the planer faces are free of loads, Knowles and Sternberg (1983) showed…”

A crack with surface elasticity in finite plane elastostatics

“…He observed that an antisymmetric solution is impossible and that crack opening at the crack tip still exists under mode II conditions. Also of great interest was the analysis of Knowles and Sternberg [1983], who studied the crack-tip field of an interface crack in a neo-Hookean bimaterial and found that the classical oscillatory singularities disappear. The asymptotic analysis of a crack in incompressible hyperelastic homogeneous materials and bimaterials was examined further by Geubelle and Knauss [1994a;1994b;1994c].…”

Dynamic crack propagation in sheets of compressible neo-Hookean material under general in-plane loading

“…The mechanical behaviour of the material described by (2.3) is of a hardening-type, as can be observed by imposing a three-dimensional homogeneous deformation corresponding to a uni-axial stress and evaluating the stress response in terms of Cauchy stresses (cf. [12] p. 269). The differences with respect to a classic incompressible neo-Hookean material are illustrated in [7], To maintain a state of plane stress, the components of the deformation gradient F are found to be [13,14] The last quantity denotes the principal stretch with the :r3-axis as the associated principal axis.…”

“…3These components must be considered as their restriction to the middle plane. A modern and accurate description of the fundamental relations of nonlinear plane stress theory can be found in a paper by Knowles and Sternberg [12].…”

“…(3.11) are [17] m' = 1 and wa(9) = Bacos9, (3)(4)(5)(6)(7)(8)(9)(10)(11)(12) where Ba are two arbitrary constants. For m!…”