An analytic solution for one-dimensional dissipational strain-gradient plasticity

Roger Young


An analytic solution is developed for the one-dimensional dissipational slip gradient equation, first described by Gurtin.. [ " On the plasticity of single crystals; free energy, microforces, plastic strain-gradients", J.Mech. Phys. Solids 48 (200) 989-1036] and then investigate numerically by Annand et al, ["A one-dimensional theory of strain-gradient plasticity: formulation, analysis, numerical results". J. Mech.Phys. Solids 53 (2005) 1798-1826].
However, we find that the analytic solution is incompatible with the zero-sliprate boundary condition ("clamped boundary condition") postulated by these authors, and is in fact excluded by the theory. As a consequence, the analytic solution agrees with the numerical results except near the boundary. The equation also admits a series of higher mode solutions where the numerical result corresponds to (a particular case of) the fundamental mode. Anand et al also established that the one-dimensional dissipational gradients strengthen the material, but this proposition only holds if zero-sliprate boundary conditions can be imposed, which we have shown cannot be done. Hence the possibility remains open that dissipational gradient weakening may also occur.



crystal plasticity, dissipational gradients, strengthening and mechanisms


Remember, for most actions you have to record/upload into this online system
and then inform the editor/author via clicking on an email icon or Completion button.
ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.