A unified treatment of strain gradient plasticity. (English) Zbl 1114.74366
Summary: A theoretical framework is presented that has potential to cover a large range of strain gradient plasticity effects in isotropic materials. Both incremental plasticity and viscoplasticity models are presented. Many of the alternative models that have been presented in the literature are included as special cases. Based on the expression for plastic dissipation, it is in accordance with M. E. Gurtin [J. Mech. Phys. Solids 48, No. 5, 989–1036 (2000; Zbl 0988.74021); Int. J. Plast. 19, No. 1, 47–90 (2003; Zbl 1032.74521)] argued that the plastic flow direction is governed by a microstress \(q_{ij}\) and not the deviatoric Cauchy stress \(\sigma_{ij}'\) that has been assumed by many others. The structure of the governing equations is of second order in the displacements and the plastic strains which makes it comparatively easy to implement in a finite element program. In addition, a framework for the formulation of consistent boundary conditions is presented. It is shown that there is a close connection between surface energy of an interface and boundary conditions in terms of plastic strains and moment stresses. This should make it possible to study boundary layer effects at the interface between grains or phases. Consistent boundary conditions for an expanding elastic-plastic boundary are as well formulated. As examples, biaxial tension of a thin film on a thick substrate, torsion of a thin wire and a spherical void under remote hydrostatic tension are investigated.
MSC:
| 74C15 | Large-strain, rate-independent theories of plasticity (including nonlinear plasticity) |
| 74C20 | Large-strain, rate-dependent theories of plasticity |
Keywords:
Strain gradients; Material length scales; Constitutive behaviour; Elastic-plastic material; Elastic-viscoplastic materialReferences:
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