Gradient Damage Analysis of a Cylinder Under Torsion: Bifurcation and Size Effects

Abstract In this work, an elastic-damage evolution analysis is carried out for a cylinder under torsion made of material obeying gradient damage model with softening. Both semi-analytical and asymptotic approaches are developed to analyze the elastic, axisymmetric bifurcation stages. We show existence fundamental branch where field asymmetric localized within finite thickness from boundary. By minimizing generalized Rayleigh quotient, time modes obtained as function length scale $\epsilon =\ell /R$ ? = ? / R involving internal radius. will then focus on these size effects by assuming that $ small parameter in setting. After justification, specific spatial temporal rescaled variables introduced boundary layer problem. It shown governed two universal functions independent scale. The simulation results approach formally justified methods.