Linearized torsional problem of plastic thin wires

•This paper develops a simple linearized strain gradient plastic flow rule.•Within the present framework the rate sensitivity function is approximated.•Size-effects in torsional deformation of plastic thin wire is presented.•Plastic strain is shown to increase along radial axis of wire’s cross section.•Our theory shows that effect of energetic length scale is pronounced. This paper develops an elegant plastic flow rule which relies on linearized constitutive relations governing the dissipative microscopic plastic stress responses in material bodies, and presents size-effects in torsional deformation of elasto-plastic thin wire using the derived flow equation. The obtained flow rule is based on strain gradient plasticity model, and is used to formulate an initial-boundary value problem describing the torsion problem of thin wire. Graphical illustration of the finite element solution of the problem shows that the accumulated plastic strain increases along radial axis of the wire’s cross section. Finally, it is observed that the effect of energetic length scale is significantly pronounced than that of the dissipative length scale during torsional deformation of the wire.