Elasticity of pentagonal wires: single disclination model versus distributed disclination model

Elasticity of pentagonal wires is analyzed in the framework of distributed disclination model. According to this model, the elastic field induced by five-fold cyclic twinning in pentagonal wires is treated as generated by a distributed disclination with uniform angular eigenstrain. Originally, the concept of distributed disclination was introduced by Howie and Marks to describe the stress-strain state of icosahedral particles in terms of the so-called Marks-Yoffe stereo-disclination. Differences between the proposed distributed disclination model and standard single disclination model are examined by an analytical technique and the finite element method. In doing so, the distribution of displacement vector and stress tensor components in pentagonal wires, as well as the dependencies of strain energy on the Poisson’s ratio of pentagonal wires, are analyzed. Analytical investigation demonstrates that both models prescribe the same expressions for mechanical stresses and strain energy, while the expressions for displacement components differ because of the plastic rotation inherent to wedge disclinations. Parametric finite element simulations are employed to estimate the accuracy of circular cross-section approximation used in both the single disclination and distributed disclination analytical models. It is demonstrated that the discrepancy between analytical results for cylindrical wires and results of finite element computations for faceted wires is ≈5 %. Besides, the finite element modeling of distributed disclination allows one to obtain the desired solution with less computational resources.