Abstract
Abstract This study represents a contribution to the local behavior of the solutions of the governing equations of elastostatics in the vicinity of corners. It contains an asymptotic investigation – within both the linear and two special nonlinear theories of plane strain – of the deformation field near a corner point that separates a free and a fixed part of the boundary. Our computations confirm that the asymptotic solutions represent the local behaviors of equilibrium states very close to the corner. In this neighborhood the linear and nonlinear theories predict very different behavior. Away from the corner the deformation gradient becomes small and the asymptotic solution in the nonlinear theory becomes – expectedly – not valid. However, in an intermediate region our numerical results obtained from both the linear and nonlinear theories show striking similarities and predict a novel behavior of the free surface.
Published Version
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