Seamless elastic boundaries for atomistic calculations

Abstract

Modeling interfacial phenomena often requires both a detailed atomistic description of surface interactions and accurate calculations of long-range deformations in the substrate. The latter can be efficiently obtained using an elastic Green's function if substrate deformations are small. We present a general formulation for rapidly computing the Green's function for a planar surface given the interatomic interactions and coupling the Green's function to explicit atoms. The approach is fast, avoids ghost forces and is not limited to nearest-neighbor interactions. The full system comprising explicit interfacial atoms and an elastic substrate is described by a single Hamiltonian and interactions in the substrate are treated exactly up to harmonic order. This concurrent multi-scale coupling provides simple, seamless elastic boundary conditions for atomistic simulations where near-surface deformations occur, such as nanoindentation, contact, friction, or fracture. Applications to surface relaxation and contact are used to test and illustrate the approach.

Mechanics of rough contacts in elastic and viscoelastic thin layers

“…Indeed, the almost totality of the boundary element methodologies formulated in the real space and presented in literature ( [54], [33], [27], [47]) relies on the half-space assumption, which consists in assuming that the thickness of the solids in contact is much larger than the contact area. In principle, boundary elements techniques derived in the Fourier space can tackle contact problems with surfaces characterised by layers of finite thickness ( [68], [66], [67]); however, systematic investigations of the effects related to the thin layer mechanics are not common in literature. Furthermore, studies performed adopting finite element methodologies ( [56], [24], [25]), molecular dynamics simulations ( [62], [61], [63]) and hybrid techniques ( [64], [65]), which intrinsically consider the bulk of the contact solids in their formulation, usually do not pay attention to the finite size effects and employs models with thickness values that are believed, on heuristic basis, to be large enough to avoid any influence given by the thickness.…”

Contact area of rough spheres: Large scale simulations and simple scaling laws

“…The calculations use an efficient Green's function method [32][33][34][35] supplemented by a padding region that prevents any effect from repeating images [36]. We use the Greens function for an isotropic solid with Poisson ratio 1/2 [18].…”

Multiscale treatment of theoretical mechanisms for the protection of hydrogel surfaces from adhesive forces

“…(C1) satisfy the boundary condition that it be 0 for negative values of p, which gives Eq. (17). The normalization factor in front of Eq.…”

“…The treatment in the previous two sections does not take into account multiscale surface roughness, and it is known that surface roughness can have a large effect on the van der Waals attraction [16,17]. In Ref.…”