Multi-Scale Modeling of Plasticity: a Coupling between Dislocation Dynamics and FEniCS

Plastic deformation of crystalline materials is the result of the collective movement of dislocations, in response of their mutual interactions and external applied loads. The study of the dislocations behavior is of fundamental importance in a wide range of fields in materials science, such as the prediction of the mechanical response of ductile materials or the plastic relaxation of strained epitaxial films. Nowadays the quantitative modeling of these systems, with an efficient mathematical and/or numerical approach, is a challenging problem. A reliable tool to study these complex phenomena is the 3D Dislocation Dynamics (DD). Nevertheless, classical DD simulations, based on an analytical description of dislocations stress field, presents limitations such as the impossibility of handling problems with complicated boundary conditions and strongly heterogeneous loading. Addressing these problems is of particular relevance in the study of thin films and micro and nano-objects, where the strong influence of the free surfaces can affect the evolution of the dislocations microstructures. Here, to overcome the limitations of classical DD simulations, we present a coupling between a 3D DD code (microMEGAS [1]) and FEniCS, exploiting the Discrete-Continuum Model (DCM) algorithm, as presented in Ref. [2] In this approach, the DD simulation code is in charge of the evolution of the dislocation microstructure and short-range dislocation-dislocation interactions, at the same time the long-range mechanical fields and dislocation interactions with the boundaries are handled by solving the mechanical equilibrium by means of the FE code. As shown in Fig.1, the coupling with a FE code succeeds in providing a numerically exact solution accounting for the presence of complex boundary conditions. Thus, it provides a reliable tool for modeling the mechanical properties at the micro and nano scale where the presence of the free surfaces influences substantially the final dislocation microstructure [3]. References [1] B. Devincre, R. Madec, G. Monnet, S. Queyreau, R. Gatti and L. Kubin, Mechanics of Nano-objects (2011) 81-100 [2] O. Jamond, R. Gatti, A. Roos and B. Devincre, International Journal of Plasticity 80, 19 (2016). [3] F. Rovaris, F. Isa, R. Gatti, A. Jung, G. Isella, F. Montalenti and H. von Kaenel, Physical Review Materials,1, 073602 (2017)