Interaction of Two Positive Disclinations in a Thin Elastic Sheet: Ridge Formation and Stress Concentration

Abstract The morphological and stress response of a thin elastic plate to the presence of two positive disclinations is investigated within the framework of von Kármán plate theory. Bifurcation plots are used to establish that the system undergoes a pitchfork bifurcation at a critical stretching-to-bending ratio (which increases with increasing defect separation) where the plate transitions from a flat to a buckled deformed configuration. With the stretching-to-bending rigidity (denoted by Γ) becoming increasingly large, a ridge appears along the line connecting the two disclinations. Along the ridge, a monopolar concentration in bending strain and a quadrupolar concentration in stress develop as Γ→∞. The former is indicative of fold formation along the ridge. The appearance of the quadrupolar stress concentration is expected in order for the fold-like feature to satisfy the transverse force equilibrium condition.