Geometrical modeling and numerical analysis of screw dislocation
نویسندگان
چکیده
This study conducts the modeling and numerical analysis of a screw dislocation in three-dimensional continuous medium. Our is based on differential geometry Weitzenböck manifold, i.e., Riemann-Cartan manifold which equips itself with non-zero torsion affine connection. Following to standard framework geometrical elasto-plasticity, we introduce three smooth manifolds representing reference R, intermediate B current S configurations express kinematics using diffeomorphisms between them. primary concern construction configuration B. For given density τ, calculated plastic distorsion Fp through integration τ by homotopy operator. yields dual frame ϑ Cartan moving frame, satisfies first structure equation Bianchi identity, simultaneously. The obtained embedding conventional Euclidean space R3 so as minimize strain energy functional. variational problem solved numerically isogeometric analysis; Galerkin method non-uniform rational B-spline basis functions. Present revealed that far-field stresses around agree quantitatively well those Volterra dislocation. A notable difference non-singularity at core. Another remarkable feature emergence hydrostatic pressure due nonlinearity. We also found surface displacements include vortex centered line. realization Eshelby twist.
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ژورنال
عنوان ژورنال: Nihon kikai gakkai ronbunshu
سال: 2021
ISSN: ['2187-9761']
DOI: https://doi.org/10.1299/transjsme.20-00409