Multi-scale modeling of plastic deformations in nano-scale materials; Transition to plastic limit

Despite the controversial debates concerning a unified theory, the continuum plasticity has evolved during the last few decades and an uncountable number of articles has been published on the subject. The proposal of Lee to decompose the deformation gradient, F, into elastic part Fe and plastic part Fp (i.e. F=FeFp) combined with the principle of maximum plastic dissipation is used in many publications to formulate the ensuing developments. However, the application of conventional plasticity into the realm of nano-structures is a new, interesting and promising subject. In this work, we have employed the decomposition, F=FpFe in contrast to the conventional decomposition F=FeFp to formulate the plasticity in nano-structures using pairwise potentials. It is shown that the former decomposition is more suitable and leads to a convenient form for stresses. The evolution of plastic variables is formulated based on the principle of maximum plastic dissipation. The numerical results compared with molecular simulations show the efficiency of method in benchmark problems.

http://onlinelibrary.wiley.com/doi/10.1002/nme.5327/full

M. Jahanshahi