The quasicontinuum (QC) method is a concurrent scale-bridging technique that extends atomistic accuracy to significantly larger length scales by reducing the full atomic ensemble to a small set of representative atoms and using interpolation to recover the motion of all lattice sites where full atomistic resolution is not necessary. While traditional QC methods thereby create interfaces between fully-resolved and coarsegrained regions, the recently introduced fully-nonlocal QC framework does not fundamentally differentiate between atomistic and coarsened domains. Adding adaptive refinement enables us to tie atomistic resolution to evolving regions of interest such as moving defects. However, model adaptivity is challenging because large particle motion is described based on a reference mesh (even in the atomistic regions). Unlike in the context of, e.g., finite element meshes, adaptivity here requires that (i) all vertices lie on a discrete point set (the atomic lattice), (ii) model refinement is performed locally and provides sufficient mesh quality, and (iii) Verlet neighborhood updates in the atomistic domain are performed against a Lagrangian mesh. With the suite of adaptivity tools outlined here, the nonlocal QC method is shown to bridge across scales from atomistics to the continuum in a truly seamless fashion, as illustrated for nanoindentation and void growth.
The efficient simulation of complex fracture processes is still a challenging task. In this contribution, an enriched phase-field method for the simulation of 2D fracture processes is presented. It has the potential to drastically reduce computational cost compared to the classical phase-field method (PFM). The method is based on the combination of a phase-field approach with an ansatz transformation for the simulation of fracture processes and an enrichment technique for the displacement field as it is used in the extended finite element method (XFEM) or generalised finite element method (GFEM). This combination allows for the application of significantly coarser meshes than it is possible in PFM while still obtaining accurate solutions. In contrast to classical XFEM / GFEM, the presented method does not require level set techniques or explicit representations of crack geometries, considerably simplifying the simulation of crack initiation, propagation, and coalescence. The efficiency and accuracy of this new method is shown in 2D simulations.
A sharp-interface model employing the extended finite element method is presented. It is designed to capture the prominent γ-γ′ phase transformation in nickel-based superalloys. The novel combination of crystal plasticity and sharp-interface theory outlines a good modeling alternative to approaches based on the Cahn–Hilliard equation. The transformation is driven by diffusion of solute γ′-forming elements in the γ-phase. Boundary conditions for the diffusion problem are computed by the stress-modified Gibbs–Thomson equation. The normal mass balance of solute atoms at the interface yields the normal interface velocity, which is integrated in time by a level set procedure. In order to capture the influence of dislocation glide and climb on interface motion, a crystal plasticity model is assumed to describe the constitutive behaviour of the γ-phase. Cuboidal equilibrium shapes and Ostwald ripening can be reproduced. According to the model, in low γ′ volume-fraction alloys with separated γ′-precipitates, interface movement does not have a significant effect on tensile creep behaviour at various lattice orientations.
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