Abstract
The paper gives an asymptotic analysis of finite plane-strain deformations near the vertex of a bi-material wedge of arbitrary angle and subjected to the traction-free surface conditions. Each of two edge-bonded dissimilar wedges is assumed to be hyperelastic with the harmonic-type strain energy density introduced by John (1960). In contrast to the results of linearized elastostatics, the deformations and stresses around the vertex of an arbitrary bi-material wedge are found to be free of oscillatory singularities within the context of finite elastostatics. A simple relation is found between the material moduli and two wedge angles that classifies the higher-order singular field into two different types. The explicit conditions for the strict positivity of the Jacobian determinant in the vicinity of the vertex are given in terms of the known material and geometric parameters independently of the loading conditions. In particular, these conditions can be easily verified for several typical kinds of bi-material wedge. Finally, the expressions for the singular field near the wedge vertex are given and the main features of deformations and stresses are summarized.
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