This review summarizes recent advances in the area of tribology based on the outcome of a Lorentz Center workshop surveying various physical, chemical and mechanical phenomena across scales. Among ...the main themes discussed were those of rough surface representations, the breakdown of continuum theories at the nano- and microscales, as well as multiscale and multiphysics aspects for analytical and computational models relevant to applications spanning a variety of sectors, from automotive to biotribology and nanotechnology. Significant effort is still required to account for complementary nonlinear effects of plasticity, adhesion, friction, wear, lubrication and surface chemistry in tribological models. For each topic, we propose some research directions.
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The Coupled Atomistic/Discrete-Dislocation (CADD) method is a concurrent multiscale technique that couples atomistic and discrete dislocation domains with the ability to pass dislocations seamlessly ...between domains. CADD has been demonstrated only in 2d plane-strain problems, for which each individual dislocation is either entirely atomistic or entirely discrete. Here, a full 3d implementation of CADD is presented, with emphasis on the algorithms for handling the description of dislocation lines that span both atomistic and continuum domains, so-called hybrid dislocations. The key new features of the method for 3d are (i) the use of an atomistic template of the dislocation core structure to transmit the proper atomistic environment of a continuum dislocation to the atomistic domain for hybrid dislocations and (ii) a staggered solution procedure enabling evolution of the hybrid dislocations. The method naturally requires calibration of discrete-dislocation Peierls stresses and mobilities to their atomistic values, implementation of a dislocation detection algorithm to identify atomistic dislocations, and computation of continuum dislocation displacement fields that provide boundary conditions for the atomistic problem. The method is implemented using the atomistic code LAMMPS and the discrete dislocation code ParaDiS within the LibMultiscale environment developed by the lead authors, and so has all the advantages of these widely-used high-performance open-source codes. Validation and application of CADD-3d are presented in companion papers.
A methodology for coupling a fully atomistic domain to a surrounding domain described by discrete dislocation plasticity, including the treatment of hybrid dislocation lines that span between the two ...domains, was presented in the first paper of this series (Anciaux et al., 2017). Here, key features of the methodology are assessed quantitatively within a quasi-static framework at 0 K. To avoid solving an expensive but standard complementary problem for the atomistic/continuum coupling of mechanical fields, which is not essential to the key features of the method, a simplified model for obtaining accurate stress and displacement fields is introduced and validated. The test problem consists of the bow-out of a single dislocation in a semi-periodic box under an applied shear stress, and excellent results are obtained in comparison to fully-atomistic solutions of the same problem.
Flexible harmonic boundary conditions have been proposed by Sinclair in the 1970s in order to overcome spurious effects on atomistic problems due to fixed boundaries. To date this method has never ...been applied to problems beyond isolated defects, such as dislocations, because it involves dense boundary matrices which become quickly unsuitable to larger problems due to their vast memory requirements. In order to apply the method for larger systems, e.g. arrangements of defects, we propose an implicit approximate representation using hierarchical matrices which have proven efficiency in the context of boundary integral equations while preserving overall accuracy. Despite its simplicity, Sinclair’s staggered method converges rather slowly if the approximate far-field harmonic response and the true nonlinear atomic response differ considerably. Starting from Sinclair’s iteration equation for the harmonic displacements, we derive a discrete variant of the well-known boundary element method (BEM) for the exterior balance equation which is then combined with the fully atomistic problem. To solve the coupled problem we propose a monolithic Newton–Krylov scheme which iterates simultaneously on all unknowns. We outline the superior performance of this method in comparison to other existing methods and to classical clamped boundary conditions with numerical examples. Further, we present guidelines for an efficient implementation into existing molecular dynamics codes.
•Efficient implementation of flexible boundary conditions for atomistic problems.•Discrete boundary element method based on lattice Green functions.•Hierarchical matrix approximation of discrete boundary element matrices.•Efficient monolithic solver for force-based atomistic/continuum coupling methods.•Considerably superior performance of flexible over clamped boundary conditions.
A direct multiscale method coupling molecular dynamics to finite element simulations is introduced to study the contact area evolution of rough surfaces under normal loading. First, a description of ...the difficulties due to using the bridging domain method at finite temperatures is discussed. This approach, which works well at low temperatures, is based on a projection, in an overlap region, of the atomic degrees of freedom on the coarser continuum description. It is shown that this leads to the emergence of a strong temperature gradient in the bridging zone. This has motivated the development of a simpler approach suitable for quasi-static contact problems conducted at constant but finite temperatures. This new approach is then applied to the normal loading of rough surfaces, in which the evolution of the real contact area with load is monitored. Surprisingly, the results show little influence of the contact area on temperature. However, the plastic events, in form of atomic reshuffling at the surface and dislocation activity, do clearly depend on temperature. The results show also a strong and temperature-dependent relaxation of the initial rough surfaces. This natural mechanism which alters atomic asperities brings to question the classical atomic description of roughness.
We study scale effects on the conductivity of crystalline contacting interfaces. The approach focuses on the role played by lattice vibrations in the thermal conductivity using finite elements and ...molecular dynamics models. A special effort is made at calibrating the continuum model directly from molecular dynamics simulations. An innovative method that uses the temperature evolution issued from an impulse boundary condition is employed to compute heat conductivity, which is notoriously known as difficult to measure. Using this approach, a parametric study is conducted on a set of contacting surfaces on which we specify asperities wavelengths. It is shown that the usual power laws that relate contact area ratio with thermal conductivity do not apply at the nanoscale.
► We present the use of digital filters to split the atomistic energy spectrum. ► Numerical examples are presented as a validation of our approach in 1D and 2D space. ► Spatial filters are better ...than time filters to perform a selective damping. ► Spatial filters are promising for MD-FE coupling at finite-temperatures.
We present the application of digital filters to split the energy spectrum of an atomistic zone simulated with molecular dynamics into low and high energy components. After a brief background on digital filters, we describe the procedure used to select a cutoff frequency for the filters. Then, a one dimensional numerical model based on the generalized Langevin equation (GLE) is used to study the system dynamics. We tested both time and spatial filters for the frictional term in GLE. Our results demonstrate that spatial filters are better than time filters to perform a selective damping within a molecular dynamics zone. Two dimensional examples validating our approach are also presented. Spatial filters should thus be favored in finite-temperature direct-coupling methods between molecular dynamics and finite elements.
We study a regularisation of Coulomb's friction law on the propagation of local slip at an interface between a deformable and a rigid solid. This regularisation, which was proposed based on ...experimental observations, smooths the effect of a sudden jump in the contact pressure over a characteristic length scale. We apply it in numerical simulations in order to analyse its influence on the behaviour of local slip. We first show that mesh convergence in dynamic simulations is achieved without any numerical damping in the bulk and draw a convergence map with respect to the characteristic length of the friction regularisation. By varying this length scale on the example of a given slip event, we observe that there is a critical length below which the friction regularisation does not affect anymore the propagation of the interface rupture. A spectral analysis of the regularisation on a periodic variation of Coulomb's friction is conducted to confirm the existence of this critical length. The results indicate that if the characteristic length of the friction regularisation is smaller than the critical length, a slip event behaves as if it was governed by Coulomb's law. We therefore propose that there is a domain of influence of the friction regularisation depending on its characteristic length and on the frequency content of the local slip event. A byproduct of the analysis is related to the existence of a physical length scale characterising a given frictional interface. We establish that the experimental determination of this interface property may be achieved by experimentally monitoring slip pulses whose frequency content is rich enough.
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