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

• Autores: Roger Young
• Localización: Anziam journal: The Australian & New Zealand industrial and applied mahtematics journal, ISSN 1446-1811, Vol. 50, Nº 3, 2009, págs. 395-406
• Idioma: inglés
• DOI: 10.1017/s1446181109000066
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• Resumen

  • 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 (2000) 989�1036] and then investigated numerically by Anand 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.