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RESEARCH PRODUCT

Shakedown Analysis Within the Framework of Strain Gradient Plasticity

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A class of rate-independent material models is addressed within the framework of isotropic strain gradient plasticity. These models exhibit a size dependence through the strengthening effects (Hall–Petch effects), whereby the yield stress is related to the effective plastic strain by a suitable second-order partial differential equation with related boundary conditions. For a perfectly plastic material with strengthening effects, the classical concepts of plastic and shakedown limit analysis do hold, which lead to size dependent plastic and shakedown limit loads according to the dictum: smaller is stronger. In the perspective of a development of direct methods for applications to small-scale structures within micro/nano technologies, a shakedown theory for perfectly plastic materials with strengthening effects, previously elaborated by the present author [51], is presented and discussed. Apart from the inevitable mathematical complications carried in by the more complex constitutive behavior of the material herein considered, the overall conceptual architecture of the shakedown theorems remain within the classical Melan and Koiter theoretical framework. Further research efforts are needed to develop specific numerical procedures for the computation of the plastic and shakedown limit loads and the concomitant collapse mechanisms.