Some properties of the dissipative model of strain-gradient plasticity

A theoretical and computational investigation is carried out of a dissipative model of rate-independent strain-gradient plasticity and its regularization. It is shown that the flow relation, when expressed in terms of the Cauchy stress, is necessarily global. The most convenient approach to formulating the flow relation is through the use of a dissipation function. It is shown, however, that the task of obtaining the dual version, in the form of a normality relation, is a complex one. A numerical investigation casts further light on the response using the dissipative theory in situations of non-proportional loading. The elastic gap, a feature reported in recent investigations, is observed in situations in which passivation has been imposed. It is shown computationally that the gap may be regarded as an efficient path between a load-deformation response corresponding to micro-free boundary conditions, and that corresponding to micro-hard boundary conditions, in which plastic strains are set equal to zero.Comment: 26 pages, 10 figure

Characterization of Generalized Young Measures Generated by Symmetric Gradients

This work establishes a characterization theorem for (generalized) Young measures generated by symmetric derivatives of functions of bounded deformation (BD) in the spirit of the classical Kinderlehrer\ue2\u80\u93Pedregal theorem. Our result places such Young measures in duality with symmetric-quasiconvex functions with linear growth. The \ue2\u80\u9clocal\ue2\u80\u9d proof strategy combines blow-up arguments with the singular structure theorem in BD (the analogue of Alberti\ue2\u80\u99s rank-one theorem in BV), which was recently proved by the authors. As an application of our characterization theorem we show how an atomic part in a BD-Young measure can be split off in generating sequences

On the mathematical formulations of a model of strain gradient plasticity

No abstract available

On the mathematical formulations of a model of strain gradient plasticity

No abstract available

A discontinuous Galerkin formulation for classical and gradient plasticity. Part 1: Formulation and analysis

A discontinuous Galerkin formulation is developed and analyzed for the cases of classical and gradient plasticity. The model of gradient plasticity is based on the von Mises yield function, in which dependence is on the isotropic hardening parameter and its Laplacian. The problem takes the form of a variational inequality of the second kind. The discontinuous Galerkin formulation is shown to be consistent and convergent. Error estimates are obtained for the cases of semi- and fully discrete formulations; these mimic the error estimates obtained for classical plasticity with the conventional Galerkin formulation

A discontinuous Galerkin formulation for classical and gradient plasticity - Part 2: Algorithms and numerical analysis

This work is the second of a two-part investigation into the use of discontinuous Galerkin methods for obtaining approximate solutions to problems of classical and gradient plasticity. Part I [J.K. Djoko, F. Ebobisse, A.T. McBride, B.D. Reddy, A discontinuous Galerkin formulation for classical and gradient plasticity. Part 1: Formulation and analysis, Comput. Methods Appl. Mech. Engrg., 196 (2007) 3881–3897] presented the formulation and analysis of such problems. This part focusses on algorithmic and computational aspects of the problem. In particular, it is shown that the predictor–corrector algorithms of classical plasticity are readily extended to the case of gradient plasticity, and to discontinuous Galerkin formulations. Conditions for convergence of the algorithms are presented, for the elastic, secant, and consistent tangent predictors. The form of the consistent tangent modulus is established for the case of gradient plasticity. A selection of numerical examples is presented and discussed with a view to illustrating aspects of the approximation scheme and algorithms, as well as features of the model of gradient plasticity adopted here