Dislocations and heat conduction are essential components that influence properties and performance of crystalline materials, yet the modelling of which remains challenging partly due to their multiscale nature that necessitates simultaneously resolving the short-range dislocation core, the long-range dislocation elastic field, and the transport of heat carriers such as phonons with a wide range of characteristic length scale. In this context, multiscale materials modelling based on atomistic/continuum coupling has attracted increased attention within the materials science community. In this paper, we review key characteristics of five representative atomistic/continuum coupling approaches, including the atomistic-to-continuum method, the bridging domain method, the concurrent atomistic–continuum method, the coupled atomistic/discrete-dislocation method, and the quasicontinuum method, as well as their applications to dislocations, heat conduction, and dislocation/phonon interactions in crystalline materials. Through problem-centric comparisons, we shed light on the advantages and limitations of each method, as well as the path towards enabling them to effectively model various material problems in engineering from nano- to mesoscale. Abbreviations: AtC: atomistic-to-continuum; BCC: body-centred cubic; BDM: bridging domain method; CAC: concurrent atomistic–continuum; CADD: coupled atomistic/discrete-dislocation; DDD: discrete dislocation dynamics; DDf-MD: discrete diffusion-molecular dynamics; DOF: degree of freedom; ESCM: embedded statistical coupling method; FCC: face-centred cubic; GB: grain boundary; XFEM: extended finite element method; MD: molecular dynamics; MS: molecular statics; PK: Peach-Koehler; QC: quasicontinuum

Theoretical analysis shows that there are several values of the phase velocity to a certain frequency of Rayleigh wave on the surface of a layered medium model, which is called the multiple mode property of Rayleigh wave. The multiple mode property of surface wave results in the complication of measured dispersion curves, especially when a soft interlayer exists in strata. This brings more difficulties to the explanation of the dispersion curves measured on this kind of site. In order to facilitate engineering application, a new method, improved equivalent homogenous half‐space method, is put forward to compute the theoretical dispersion curve of a layered medium model based on the equivalent homogenous half‐space theory. This new method does not need to deal with the multiple value problem of the phase velocity, and the phase velocity resulting from this method can reflect the synthetic effect of all modes of Rayleigh waves. The inverse fitting program is compiled based on the improved equivalent homogenous half‐space method, which has gotten a very good effect in an engineering application.

This study introduces a novel two-step approach for the probabilistic prediction of stress–strain curves of materials at the nanoscale, specifically in terms of material volume. Molecular dynamics (MD) simulations are first conducted for materials of varying sizes to acquire stress–strain data. A multioutput Gaussian process with Bayesian analysis is then employed to model the stress–strain behavior and predict stress and strain values at critical deformation points (i.e., yielding, hardening, and failure) for different material sizes. By incorporating comprehensive uncertainty estimates alongside the probabilistic predictions, this probabilistic machine learning algorithm enables precise forecasting of the stress–strain behavior of materials beyond the typical material volume range covered by MD simulations, addressing the critical inherent size limitations issue in atomistic simulations. In this study, the effectiveness of the method is rigorously validated using pure copper, which possesses abundant experimental stress–strain data. However, the methodology is not limited to a specific material and can serve as a robust and versatile tool for probabilistic prediction of the mechanical behavior of materials at the nanoscale across various applications in the field of materials science and engineering.