“…As discussed in section (3.e.i), the evaluation of C~ carries a significant cost, and reducing the frequency of their calculation is essential to the feasibility of the overall simulation. Another potential speed-up is to only compute an approximation of C~ derived from the interatomic potential expression omitting the stress fluctuation term [27]. Figure 7.Solving quasi-static equilibrium of continuum mechanics implies evolving the continuum system using the stiffness matrix K of the associated linearized system of equations; which relies on the initial estimation of Cfalse~ at equilibrium (blue) or on updated estimations all along the deformation path using the atomistic system (red); reducing the frequency update leads to larger error on the estimation of u in between prediction-correction steps.…”
Section: Scale-bridging For Inelastic Mechanicsmentioning
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’.
“…As discussed in section (3.e.i), the evaluation of C~ carries a significant cost, and reducing the frequency of their calculation is essential to the feasibility of the overall simulation. Another potential speed-up is to only compute an approximation of C~ derived from the interatomic potential expression omitting the stress fluctuation term [27]. Figure 7.Solving quasi-static equilibrium of continuum mechanics implies evolving the continuum system using the stiffness matrix K of the associated linearized system of equations; which relies on the initial estimation of Cfalse~ at equilibrium (blue) or on updated estimations all along the deformation path using the atomistic system (red); reducing the frequency update leads to larger error on the estimation of u in between prediction-correction steps.…”
Section: Scale-bridging For Inelastic Mechanicsmentioning
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’.
“…Natural phenomena show multiscale character in space and time. 'Continuum-on-atomistic' multiscale coupling methods have achieved great popularity today [14]. Actually, when considering electromagnetic input parameters, finite element methods are able now to stand alone when describing optical properties of nanoscale structures [15].…”
A brief theory and simulation overview for the purpose of design is presented with examples applies to modeling the physical properties, behavior, and phenomena of nanomaterial. This review paper constructs perspectives that consider coupling traditional domains of simulation by novel pathways to produce accurate representations of nanomaterial properties, behavior and phenomena. It is all about size scaling and how different approaches are able to simulate, integrate or simply pass the baton to the next level of complexity. In macroscopic world, the atomic or molecular information alone may not be directly useful. Nor is the bulk information useful in the microscopic world without intimate knowledge of molecular makeup. Therefore, when designing Nanomaterials, knowledge of properties spanning the complete range of size is the prerequisite of a recommended self-consistent approach. In fact, regarding applications in both industry and academia, the simulation first approach often can lead to great savings in time. This review paper focuses mostly on optical and electronic properties but a section is added that provides a segue into mechanical properties for future consideration.
“…The approach used in our work is rooted in the Heterogeneous Multiscale Method [70,71] (HMM) as implemented for a Hierarchical Multiscale Simulation (HMS) of an energetic material [72][73][74][75]. The HMM approach has also been used for coupling of atomistic simulations to continuum simulation for other materials, such as metals [76][77][78][79]. Application of HMM to a particular problem relies on careful specification of the information provided to, and required from, the microscale simulation, which in this work will be the equation of state (EOS) response for an energetic material.…”
We present new capabilities for investigation of microstructure in energetic material response for both explicit large‐scale and multiscale simulations. We demonstrate the computational capabilities by studying the effect of porosity on the reactive shock response of a coarse‐grain (CG) model of the energetic material cyclotrimethylene trinitramine (RDX), the non‐reactive equation of state for a porous representative volume element (RVE) of CG RDX, and utilization of available supercomputing resources for speculative sampling to accelerate hierarchical multiscale simulations. Small amounts of porosity (up to 4 %) are shown to have significant effect on the initiation of reactive CG RDX using large‐scale reactive dissipative particle dynamics simulations. Non‐reactive RVEs are shown to undergo a porosity‐dependent pore collapse at hydrostatic conditions, and an existing automation framework is shown to be easily modified for the incorporation of microstructure while retaining reliable convergence properties. A novel predictive sampling method based on use of kernel density estimators is shown to effectively accelerate time‐to‐solution in a multiscale simulation, scaling with free CPU cores, while making no assumptions about the underlying physics for the data being analyzed. These multidisciplinary studies of distinct yet connected problems combine to provide methodological insights for high‐fidelity modeling of reactive systems with microstructure.
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