Abstract
This paper is devoted to the theory of gradient plasticity. Our attention is focussed on the description of the constitutive equations, on the formulation of the governing equations in terms of the energy potential and the dissipation potential of the solid. The evolution equation is discussed for quasi-static responses. A time-discretization by the implicit scheme of the evolution equation leads to the study of the incremental problem which is different from the rate problem. The incremental problem and associated incremental variational principles are discussed in relation with some existing results of the literature.
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Nguyen, QS. (2017). Quasi-static Evolution, Variational Principles and Implicit Scheme in Gradient Plasticity. In: Frémond, M., Maceri, F., Vairo, G. (eds) Models, Simulation, and Experimental Issues in Structural Mechanics. Springer Series in Solid and Structural Mechanics, vol 8. Springer, Cham. https://doi.org/10.1007/978-3-319-48884-4_7
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DOI: https://doi.org/10.1007/978-3-319-48884-4_7
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