Multiscale Phase-Field Modeling of Fracture in Nanostructures

The scientific community has witnessed, lately, a tremendous progress in the fabrication and synthesis of nanomaterials. As a result, it is essential to develop new and efficient numerical techniques that are capable of modeling the behavior of materials at nanoscale with sufficient accuracy. In this work, a novel approach is presented for the multiscale analysis of brittle failure in nanostructures using the phase-field modeling. The specimen at microscale is discretized using finite elements (FEs), whose integration points lie in the representative volume elements (RVEs) at nanoscale. The displacement computed in upper scale for a microstructure that contains an evolving crack is imposed on the boundaries of the RVE in lower scale. On the other hand, the stresses and material properties obtained for the RVE in lower scale are transferred to upper scale to compute stiffness matrices and load vectors. The evolution of the phase-field variable indicates the initiation and propagation of cracks at microscale. In order to avoid time-consuming molecular dynamics (MD) simulations at nanoscale in each step of the analysis, the Mooney-Rivlin material model is used to simulate the behavior of Aluminum (AL) nanostructure at this scale. The approach that is utilized to compute the material constants and the formulation for the multiscale technique combined with the phase-field modeling in upper scale are described in detail. It is discussed how the phase-field variable in microstructure is evolved based on the properties of the RVE in nanostructure. Many numerical examples are presented to demonstrate the application of the proposed multiscale technique in the solution of engineering problems.