On the corner behavior of a non-linear elastic wedge under mixed boundary conditions

• We consider a mixed boundary-value problem for a non-linear elastic wedge.
• We obtain asymptotic expansion of deformation field for wedge angle α in (0, 2π).
• We predict unexpected behavior of deformed free surface that is physically possible.
• Depending on α, none, one, or, two singular terms occur in the asymptotic expansion.
• The expansion results either agrees or improves with previously published results.

This study concerns the local behavior of the solutions of the governing equations of non-linear elastostatics in the vicinity of the corner of a wedge-shaped region of angle α∈(0,2π]α∈(0,2π]. It contains an asymptotic investigation in the plane strain regime – using a subclass of non-linear harmonic elastic solids that have a proper asymptotic constitutive structure in the vicinity of the corner – of the deformation field near the corner point that separates a free from an adjoining fixed segment of the boundary. It is well-known that, as the corner point is approached, the singular field behavior predicted by the classical linear theory of elasticity yields oscillatory deformations that are not injective. This anomalous behavior is related to a spurious self-intersection anomaly. Using a proper constitutive structure within a subclass of non-linear harmonic materials in the vicinity of the corner, we obtain an asymptotic expansion of the deformation field for which the foregoing anomalous behavior is avoided. The conditions on this field which guarantee injectivity lead to an unexpected behavior of the deformed free surface that is physically possible. In the particular case of α=πα=π, the second-order expansion of the deformation field agrees with its counterpart found elsewhere in the literature. For another particular case, concerning α=π/2α=π/2, the second-order expansion is an improvement over its counterpart found in the literature.