Some remarks on standard gradient models and gradient plasticity. (July 2015) - Nguyen, Quoc-Son
The standard gradient models, originally introduced in the works of Gurtin ( Physica D 1996; 92: 178) and Frémond and Nedjar ( Int J Solids Struct 1996; 33: 1083) have been studied intensively in the last few decades for various applications in plasticity, damage mechanics and multi-phase analysis. In this paper, these models are revisited and discussed in relation with some classical descriptions of solids such as plasticity and visco-plasticity. The constitutive equations of such a model and the governing equations for a solid have been initially derived by these authors from an extended virtual work principle. Without this starting point, it is shown here that these equations appear as a generalized Biot equation for the solid and can be obtained directly from the global expression of the energy and dissipation potentials. This result gives the possibility to write the governing equations for standard gradient models of any order. These models also appear as a simple generalization of classical descriptions in solid mechanics. As an example, for a time-independent process such as incremental plasticity, our attention is focused on the constitutive modeling and on the governing equations of the response. It is shown that an elastic regularization can be introduced to avoid some theoretical and numerical difficulties which are well known in the classical theory of rigid plasticity.