The heterogeneous multiscale method applied to inelastic polymer mechanics

Abstract

Mechanisms emerging across multiple scales are ubiquitous in physics and methods designed to investigate them are becoming essential. The heterogeneous multiscale method (HMM) is one of these, concurrently simulating the different scales while keeping them separate. Owing to the significant computational expense, developments of HMM remain mostly theoretical and applications to physical problems are scarce. However, HMM is highly scalable and is well suited for high performance computing. With the wide availability of multi-petaflop infrastructures, HMM applications are becoming practical. Rare applications to mechanics of materials at low loading amplitudes exist, but are generally confined to the elastic regime. Beyond that, where history-dependent, irreversible or nonlinear mechanisms occur, not only computational cost but also data management issues arise. The micro-scale description loses generality, developing a specific microstructure based on the deformation history, which implies inter alia that as many microscopic models as discrete locations in the macroscopic description must be simulated and stored. Here, we present a detailed description of the application of HMM to inelastic mechanics of materials, with emphasis on the efficiency and accuracy of the scale-bridging methodology. The method is well suited to the estimation of macroscopic properties of polymers (and derived nanocomposites) starting from knowledge of their atomistic chemical structure. Through application of the resulting workflow to polymer fracture mechanics, we demonstrate deviation in the predicted fracture toughness relative to a single-scale molecular dynamics approach, thus illustrating the need for such concurrent multiscale methods in the predictive estimation of macroscopic properties. This article is part of the theme issue ‘Multiscale modelling, simulation and computing: from the desktop to the exascale’.

Toward High Fidelity Materials Property Prediction from Multiscale Modeling and Simulation

“…The proposed workflow [86] computes the dynamic equilibrium of mechanical forces in a continuum structure using the finite element method (FEM). In a classical FEM approach the local constitutive relation between stresses and strains is a series of phenomenological mathematical equations, but in the present case it is replaced by a molecular dynamics (MD) simulation (see figure 7).…”

“…In an attempt to analyse or predict mechanical properties related to failure, fatigue, energy dissipation (and many other situations), capturing these inelastic mechanisms is of the utmost importance. In our recent work, we introduced modifications to the standard HMM implementation to capture history dependent mechanical behaviour, including non-linear and irreversible mechanisms[86]. In turn, our approach is able to track the evolution of the structure at the atomistic scale associated with each continuum location.Although, the initial atomistic systems are identical, they diverge rapidly due to different mechanical loading history.…”

Introducing VECMAtk - Verification, Validation and Uncertainty Quantification for Multiscale and HPC Simulations

“…For nanocomposite systems, the characteristic time and length of its nanostructure and macrostructure are so far apart, their respective dynamics can be simulated separately. We use DealLAMMPS [23,24], a new program that simulates the nanoscale with LAMMPS molecular dynamics, and the macroscale is simulated using deal.II, a finite element solver. Boundary information is passed from the FEM model to the LAMMPS simulations, the stresses arising from these changes are used to propagate the macroscale model.…”

The Role of Graphene in Enhancing the Material Properties of Thermosetting Polymers

“…Having investigated the influence of a single sheet of graphene, we now simulate a macroscopic structure integrating the effect of a large number of them. Drawing on a novel application of the heterogeneous multiscale method to the inelastic behavior of amorphous materials, we simulated the behavior of a thin rectangular shell of epoxy nanocomposite of dimensions 150 mm× 100 mm× 5 mm for 0.2 ms. Our approach reduces this system to two significant scales. On the one hand, we include the atomistic scale characterized by several replicas of the molecular dynamics models (see Figure a).…”

“…Interestingly, this mechanism is fundamentally different from that observed in thermoplastic nanocomposites, where polymer is absorbed on and tightly bound to the surface of the 2D nanoparticles, leading to consistent enhancement of the strength. Multiscale analysis of the nanocomposite uncovers enhanced elastic capabilities due to inclusion of graphene particles. At relatively low amplitude oscillations, the nanocomposite dissipates up to 70% less of the energy caused by the impact in the form of strain energy.…”