Data from: Geometrical frustration in nonlinear mechanics of screw dislocation

The stress singularities and reliance on linear elasticity pose
significant challenges in comprehending the mechanism of the formation of
stress fields around dislocations. In this study, we use differential
geometry and calculus of variations for the mathematical modelling and
numerical analyses for the mechanics of screw dislocations. We express the
kinematics of dislocations by using a diffeomorphism of the Riemann-Cartan
manifold, which equips the Riemannian metric and affine connection. We
formulate the function of the Cartan first structure equation for solving
plastic deformation of dislocations, while we employ the stress
equilibrium equations for nonlinear elasticity. To solve this nonlinear
problem, we conduct isogeometric analysis with NURBS basis functions. We
implement this using C++. The analysis results obtained by this
implementation show that the stress fields effectively eliminate the
singularity along the dislocation line and exhibit excellent agreement
with Volterra's theory outside the dislocation core. Furthermore, by
utilising the mathematical properties of the Riemann-Cartan manifold and
smoothness of the NURBS functions used in the isogeometric analysis, we
show that geometrical frustration is the direct source of dislocation
stress fields, and the Ricci curvature determines the symmetry of stress
fields. These results demonstrate the duality between stress and
curvature, a mathematical hypothesis posed in previous studies.