Challenges to marrying atomic and continuum modeling of materials

Modeling dislocations and heat conduction in crystalline materials: atomistic/continuum coupling approaches

“…We remark that any errors present in the static implementation will remain, if are not amplified, in the dynamic setting, which introduces new challenges to be discussed in the next subsection. For example, in terms of the governing formulation, the energy-based methods are built onminimising a well-defined energy functional for static problems [12]. However, they are inevitably accompanied by non-physical 'ghost forces' stemming from the combination of two energy functionals from different models, e.g.…”

“…Cai et al [69], E and Huang [70], Yang et al [71], and Ramisetti et al [72] focused on improving the transmission of waves across the atomistic/continuum domain interface. It is known that wave propagation originated in the atomistic domain may not be fully transmitted to the continuum domain and may be reflected back, resulting in a localised, non-physical heating in the former [12], for several reasons: (i) different governing equations lead to differences in vibrational properties between the atomistic and continuum domains, resulting in aphysical scattering at the interface [48]; (ii) the continuum domain, with a lower numerical resolution that may be due to a larger characteristic length of the elements, does not naively receive all wave information from the atomistic domain that has a finer resolution and allows a shorter wavelength; and (iii) the pad region in the continuum domain, which is used to provide boundary conditions for the atomistics, usually lacks thermal motion which may have consequences on the dynamics of adjacent atoms.…”

“…For both types of mesh-refining methods, one common challenge is the geometric complexity of the mesh and its adaption, due to either the interelement compatibility requirement and/or enrichment strategies in the continuum, or the information passing techniques between the two domains [75]. In addition, in cases where continuous finite elements with high-order shape functions are used to represent a defected lattice, the assignment of atom coordinates from a continuum may not be unique and straightforward [12].

Figure 1.Snapshots of a QC simulation of nanoindentation on a Cu single crystal at a loading rate of m/s.

…”

“…In most atomistic/continuum coupling domain decomposition methods, atomistic domains, in which atoms are updated in the same way as in atomistic methods such as molecular dynamics (MD) and molecular statics (MS), are employed where explicit descriptions of nanoscale structures and phenomena are essential [4]; otherwise, continuum domains are employed in various ways to reduce computational cost [1]. In the last 15 years, a plethora of reviews have been dedicated to analysing and comparing the theoretical foundations of different multiscale models [5][6][7][8][9][10][11][12]. For example, 14 atomistic/continuum coupling techniques were implemented in 2009 by Miller and Tadmor [13] to simulate a Lomer dislocation dipole for which the theories, numerical accuracy, and efficiency of these methods are compared.…”

“…In this paper, we review multiscale modelling of dislocations and heat conduction in crystalline materials using atomistic/continuum coupling approaches. We remark that most concurrent multiscale methods, with some exceptions [15][16][17][18], are only applicable to crystalline materials because their atomic-level structures facilitate the atomistic/continuum coupling [12]. We purposely choose dislocations, either the Volterra dislocation (1D linear defect) or the extended dislocation (2D planar defect), in part because of their typicalities in representing a wide range of lattice defects.…”