Advanced Modeling and Machine Learning - Advanced Cooling Technologies

Advanced Modeling

Peridynamics-Based Meshless Modeling

Peridynamics (PD) is a recently introduced non-local reformulation of classical elasticity theory for modeling materials with discontinuities such as cracks [1]. The theory replaces the partial differential equations of classical solid mechanics with integro-differential equations. The equations are based on a model which treats the internal forces within a body as a network of interactions between material points. The governing equation for the peridynamics material points is given by the local conservation of linear momentum as,

The numerical discretization of the governing equation can be cast into a meshless particle (Lagrangian-type) approach, which allows for simulation of discontinuities like crack without any need for re-meshing the domain. The mathematical structure of the PD approach automatically enables simulation of cracks propagation and failure, without the need for complicated crack path algorithms like that of XFEM or cohesive element method.

PD framework can also be used to model multiphysics problems, by expanding the constitutive model to include thermal, electrical, and diffusive effects. ACT has developed PD based models for prediction of damage phenomenon in the following areas:

1. Corrosion fatigue damage in metals

2. Progressive damage in thick composites

3. Crack propagation and failure in engineering metals and alloys

Peridynamics is very well suited to mode damage and crack paths in fiber reinforced composites (FRCs). Composites exhibit complex failure mechanisms due to their inherent anisotropy (fiber, matrix phases) and damage aspects like matrix cracking, fiber breakage, fiber-matrix shear and delamination. The exact nature of damage evolution and failure depends on complex interactions between the fiber, matrix phases of each ply and inter-ply interactions, in response to the loading environment.

Publications:

Corrosion Damage and Corrosion Fatigue

Corrosion and its synergistic interactions with mechanical loading are a major cause of damage and failure of structural components in aging Navy aircraft fleet and infrastructure, with adverse implications on both operational safety and ownership costs. Traditional tools for predicting corrosion-related damage are based on analytical models and yield large uncertainties in service environments.

ACT developed a micro-chemically sensitive peridynamics model for corrosion damage and resulting crack propagation phenomena under synergistic effects of corrosion and mechanical loading. The approach is based on nonlocal peridynamics theory that replaces governing equations of classical continuum mechanics with integro-differential equations that are easy to solve across discontinuities like cracks. The framework is able to capture corrosion pitting, nucleation, crack path propagation under synergistic influence of corrosion and mechanical loading, without the need to re-mesh the domain or special numerical treatments. The developed peridynamic approach provides a physics-based alternative to conventional theories and enables crack propagation studies in corrosive environments. The approach is capable of modeling stress corrosion cracking (SCC), Hydrogen Embrittlement (H-Embrittlement), Corrosion Fatigue (CF).

The resulting corrosion toolkit provides a physics-based framework for modeling corrosion influence on naval aircraft components and its impact to service life.

Publications:

Molecular Dynamics for Nano-scale Phenomena

Molecular Dynamics (MD) is an advanced simulation method where the trajectories of atoms are tracked as they move about due to the attractive and repulsive forces between neighboring atoms. Using interatomic potentials that describe the forces between atoms, Newton’s Second Law of Motion, and subjecting the ensemble of atoms to the desired temperature and pressure, the trajectories are computed by numerical integration of the equations of motion. Based on these calculated trajectories, transport properties, structural characteristics and reaction pathways can be predicted for various materials, liquids and gas mixtures. Using modern computing processors and parallel processing techniques, MD simulations can calculate systems with millions of atoms, large enough to model complex material systems and chemical reactions, for time periods up to 10′s of nanoseconds, long enough to calculate time-averaged transport properties and kinetics.

Using molecular dynamics simulations with a reactive force field (ReaxFF), ACT team generated models of amorphous carbon (a-C) at a wide range of densities (from 0.5 g/cc to 3.2 g/cc) via the ‘liquid-quench’ method. A systematic study is undertaken to characterize the structural features of the resulting a-C models as a function of carbon density and liquid quench simulation conditions: quench rate, type of quench (linear or exponential), annealing time and size of simulation box. The resulting char structures were subsequently.

Publications:

Electro-Thermal for Semiconductors

As transistor sizes continue to decrease, thermal engineers are investigating ways to decouple the electron and phonon transport physics that are typically combined in the classical Fourier’s Law of Conduction. At the various semiconductor/metallic interfaces, heat traveling in the phonons in the semiconductor material must first conduct heat to the phonons in the metal. The phonons in the metal must then transfer heat to the electrons in the metal. These extra transport steps add additional resistances that are not present if only contact resistance and Fourier-type conduction are included. MD, ab initio and other advanced modeling techniques can be used to estimate the atomic structure at the interface and the “bottlenecks” that occur when conducting between phonons and electrons at the interface between two materials.

Electronics cooling is currently one of the largest areas for thermal research and development. The decreasing size and increasing power consumption in transistors have led to many thermal challenges. MD, ab initio and BTE modeling techniques are required to accurately predict the chip-level thermal transport process. Accurate modeling of the electron conduction, phonon conduction, and energy transfer between electrons and phonons is required to capture the heating process in a transistor. This technical understanding is important since the relative proportions of electron conduction, phonon conduction and electron to phonon conversion are important.

ACT has developed several in-house models and simulation codes to successfully simulate multiphysics behavior in semiconductor materials made of SiC and GaN. These tools enable simulation of coupled field problems and provide previously unavailable insights to materials and thermal engineers involved in semiconductor chip design.

Publications:

Angie Fan et, al., “2-D Simulation of Hot Electron-Phonon Interactions in a Submicron Gallium Nitride Device Using Hydrodynamic Transport Approach”, ASME 2012 Summer Heat Transfer Conference, Puerto Rico, USA, July 8-12, 2012, https://www.1-act.com/2-d-simulation-of-hot-electron-phonon-interactions-in-a-submicron-gallium-nitride-device-using-hydrodynamic-transport-approach/

Reactive Molecular Dynamics and Accelerated Techniques for Computational Chemistry

Reactive molecular dynamics methods refer to a class of MD methods that enable the simulation of chemical reactions and chemistry-based nanoscale phenomena with accuracy to ab initio methods. While classical MD provides a powerful tool to simulate nanoscale spatiotemporal phenomena and bulk properties, they lack the ability to simulate chemical reactions. On the other hand, quantum mechanics (QM) based ab initio methods enable simulations of chemical reactions but are computationally expensive and limited to a 10’s of atoms. To circumvent this problem, reactive MD methods have been developed that use empirical interatomic potentials with the capability to locally mimic the quantum effects of a bond change due to chemical reactions.

Reactive MD methods use a force field description which is ‘trained’ to reproduce reactions determined from quantum mechanical calculations and experimental data. A class of such methods uses concept of bond order to represent the forces between interacting atoms in a chemical system. Typical examples of such force descriptions include Reactive Empirical Bond-Order potential (REBO), Adaptive Intermolecular Reactive Empirical Bond-Order potential (AIREBO), Reactive Force Field (ReaxFF) potential. The bond order-based definition of atomic and molecular interactions excludes the need for predefined reactive sites and allows for dynamic description of bond breaking and formation. Recent progress in reactive potentials enables study of wide range of materials such as hydrocarbons, polymers, silica systems, nitramines and catalysis phenomena.

ACT has developed a reactive MD-based computational framework to investigate chemical behavior of polymer composite materials subject to thermo-chemical degradation. The approach makes use of reactive MD simulations and novel reactive force fields to obtain information on chemical products, rate of formation of these products and reaction pathways. The framework has been developed and applied to study pyrolysis (thermal deposition) phenomena for two types of materials: (i) ablative phenolic heat-shield composite used in space-craft reentry vehicles, and (ii) ablative rubber insulator of solid rocket motor type engines.

Accelerated Reactive Molecular Dynamics Simulation Framework

Conventional reactive MD methods are limited to high temperature simulations and suffer from small timestep problem inherent to MD (due to stiffness of evolution equations). Simulation temperatures of reactive MD studies are usually performed at temperatures of ~3000K with timestep of order of 0.25 femtoseconds. Consequently, simulations can probe 100’s of picosecond of dynamics to a maximum of a nanosecond. However, most interesting phenomena at nanoscale evolve over longer times and sometimes requires lower temperature studies. To address these challenges, ACT has recently developed Accelerated Reactive Molecular Dynamics Simulator (ARMS), a computational tool which can be used to investigate material chemistry at low temperatures using reactive molecular dynamics simulation. The framework makes use of multi-core processors to track many replicas of the system in parallel, effectively parallelizing the time required to simulate chemical reactions at low temperature. The methodology has been used to probe low temperature (of ~1750K) pyrolysis chemistry of ablative heat-shield materials typical to space-craft re-entry vehicles and solid rocket motor insulation. We find that the chemistry at low-temperature is significantly different from high temperatures and results in distinct reaction pathways.

ACT’s custom tools for Chemical Kinetics of Complex Phenomena

To enable molecular modeling of complex chemical phenomena resulting from multiple active species and long-chain polymers is limited by uncertainties in the reaction rate parameters, which increase rapidly with the number of active species and/or reaction pathways. Reactive molecular dynamics simulations have the potential to help obtain in-depth information on the chemical reactions that occur between the polymer (e.g., ablative material) and the multiple active species in an aggressive environment. ACT team developed two custom tools that post-processes reactive MD simulation data and enables the identification of chemical kinetics data and reduced models of chemical kinetics.

1. Molecular Fraction Analysis Custom Toolkit (MolfrACT) – for extracting chemical species, reaction pathways and energetics information.

2. Kinetic Analysis Custom Toolkit (KinACT) – tools for reduction of chemical kinetics data to obtain reduced chemical kinetics.

The reaction-related information is extracted via an iterative scheme christened CReSIS (Consistent Reaction Stoichiometry via an Iterative Scheme). The framework was validated by simulating iso-octane combustion and comparing against experimentally reported pathways for iso-octane combustion. Subsequently, the framework was employed to investigate ablation chemistry of ethylene-propylene-diene-monomer (EPDM) rubber ablatives.

Publications:

Smooth Particle Hydrodynamics for Process Modeling

ACT developed a meshless approach that utilizes Smoothed Particle Hydrodynamics (SPH) to obtain a physics-based model capable of capturing the thermo-mechanical behavior of Linear Friction Welding (LFW) process in 3D. Linear friction welding (LFW) is a solid-state joining process in which a weld between two metals is formed by the combined action of heating via plastic deformation and forming force that creates a weld interface. The technique is increasingly attracting attention in aerospace industry, due its several advantages like absence of solidification defects, no requirement for external heat source, and the mechanical and fatigue properties of the weld being equivalent or surpassing the parent material. Due to large deformation, commercially available software tools are limited to modeling of LFW in 2D using Finite Element Method (FEM) with adaptive mesh controls. The developed models were employed to simulate and investigate flash formation and burn-off distance of LFW of Ti-6Al-4V workpieces. The SPH simulation results agreed well with FE simulation and experimental data.

Publications:

Q.Truong, S. K. Rokkam and M. Eff, “A Smoothed Particle Hydrodynamics Approach for Efficient 3D Process Modeling of Linear Friction Welding”, AIAA 2023-0526, 2023. https://arc.aiaa.org/doi/abs/10.2514/6.2023-0526

Thermal Challenges?

Contact ACT