Jay Oswald

Analysis of periodic dislocation networks using x-ray diffraction and extended finite element modeling

We combine the extended finite element method with simulations of diffracted x-ray intensities to investigate the diffusely scattered intensity due to dislocations. As a model system a thin PbSe epitaxial layer grown on top of a PbTe buffer on a CdTe substrate was chosen. The PbSe film shows a periodic dislocation network where the dislocations run along the orthogonal ⟨110⟩ directions. The array of dislocations within this layer can be described by a short range order model with a narrow distribution.

Explicit Dynamic Finite Element Method for Predicting Implosion/Explosion Induced Failure of Shell Structures

A simplified implementation of the conventional extended finite element method (XFEM) for dynamic fracture in thin shells is presented. Though this implementation uses the same linear combination of the conventional XFEM, it allows for considerable simplifications of the discontinuous displacement and velocity fields in shell finite elements. The proposed method is implemented for the discrete Kirchhoff triangular (DKT) shell element, which is one of the most popular shell elements in engineering analysis. Numerical examples for dynamic failure of shells under impulsive loads including implosion and explosion are presented to demonstrate the effectiveness and robustness of the method.

A pressure-transferable coarse-grained potential for modeling the shock Hugoniot of polyethylene

We investigate the thermomechanical response of semi-crystalline polyethylene under shock compression by performing molecular dynamics (MD) simulations using a new coarse-graining scheme inspired by the embedded atom method. The coarse-graining scheme combines the iterative Boltzmann inversion method and least squares optimization to parameterize interactions between coarse-grained sites, including a many-body potential energy designed to improve the representability of the model across a wide range of thermodynamic states. We demonstrate that a coarse-grained model of polyethylene, calibrated to match target structural and thermodynamic data generated from isothermal MD simulations at different pressures, can also accurately predict the shock Hugoniot response. Analysis of the rise in temperature along the shock Hugoniot and comparison with analytical predictions from the Mie-Grüneisen equation of state are performed to thoroughly explore the thermodynamic consistency of the model. As the coarse-graining model affords nearly two orders of magnitude reduction in simulation time compared to all-atom MD simulations, the proposed model can help identify how nanoscale structure in semi-crystalline polymers, such as polyethylene, influences mechanical behavior under extreme loading.

Molecular Dynamics (MD) and Coarse Grain Simulation of High Strain-Rate Elastomeric Polymers (HSREP)

In this chapter, an overview is provided of the all-atom and coarse-grained computational methods and tools used to investigate the superior shock wave dispersion/attenuation capacity of nanosegregated polyurea. This class of HSREP consists of (high glass-transition temperature, Tg) nanometer-sized rod-shaped, discrete, so-called hard domains which are embedded into a (low Tg) highly compliant, so-called soft matrix. Direct simulations of the interactions of shock waves (of different strengths) with the host material using all-atom and coarse-grained molecular-dynamics methods enables identification and quantification of the key viscous or inelastic deformation and microstructure-altering processes occurring at the shock front. Among these processes, the ones which are most likely responsible for the dispersion of fully supported shock waves in polyurea have been identified as shock-induced coordinated shuffle-like motion of the soft-matrix chain-segments behind the shock front, densification and crystallization of hard domains, and breakage and regeneration of the hydrogen bonds within the hard domains. In addition, in the case of blast-induced shock waves, it is shown that the “shock wave capture and neutralize” process by the release-waves can play an important role and that the efficacy of this process is greatly affected by the polyurea molecular weight and its synthesis route. This chapter presents developments in the molecular modeling and simulation of elastomeric polymers to link the microstructural and chemical features of polyurea to its macroscopic mechanical properties. A bead-spring model is first presented to qualitatively illustrate the importance of the hard domains of polyurea to its mechanical performance and demonstrate how the interaction energy between hard segments influences the microphase separation and morphology of hard domains. Next, a more sophisticated coarse-grained model of polyurea, calibrated in a bottom-up fashion from fully atomistic molecular dynamics simulations, is presented. This systematically coarse-grained model is parameterized to match structural distributions calculated from atomistic simulations by using the iterative Boltzmann inversion method. A method for dynamically rescaling the coarse-grained simulations to accurately predict the viscoelastic stress relaxation function is developed by matching the atomistic and coarse-grained diffusion rates. Analysis shows that quantitative predictions of the stress relaxation response of a complicated polymer can be computed from such multiscale approaches with reasonable accuracy. In conclusion, several outstanding challenges in coarse-grained modeling of polymers and bridging such models with continuum models are presented.

Molecular Dynamics (MD) and Coarse Grain Simulation of High Strain-Rate Elastomeric Polymers (HSREP): Molecular and Coarse-Grained Methods for Microstructure-Property Relations in HSREP

In this chapter, an overview is provided of the all-atom and coarse-grained computational methods and tools used to investigate the superior shock wave dispersion/attenuation capacity of nanosegregated polyurea. This class of HSREP consists of (high glass-transition temperature, Tg) nanometer-sized rod-shaped, discrete, so-called hard domains which are embedded into a (low Tg) highly compliant, so-called soft matrix. Direct simulations of the interactions of shock waves (of different strengths) with the host material using all-atom and coarse-grained molecular-dynamics methods enables identification and quantification of the key viscous or inelastic deformation and microstructure-altering processes occurring at the shock front. Among these processes, the ones which are most likely responsible for the dispersion of fully supported shock waves in polyurea have been identified as shock-induced coordinated shuffle-like motion of the soft-matrix chain-segments behind the shock front, densification and crystallization of hard domains, and breakage and regeneration of the hydrogen bonds within the hard domains. In addition, in the case of blast-induced shock waves, it is shown that the “shock wave capture and neutralize” process by the release-waves can play an important role and that the efficacy of this process is greatly affected by the polyurea molecular weight and its synthesis route. This chapter presents developments in the molecular modeling and simulation of elastomeric polymers to link the microstructural and chemical features of polyurea to its macroscopic mechanical properties. A bead-spring model is first presented to qualitatively illustrate the importance of the hard domains of polyurea to its mechanical performance and demonstrate how the interaction energy between hard segments influences the microphase separation and morphology of hard domains. Next, a more sophisticated coarse-grained model of polyurea, calibrated in a bottom-up fashion from fully atomistic molecular dynamics simulations, is presented. This systematically coarse-grained model is parameterized to match structural distributions calculated from atomistic simulations by using the iterative Boltzmann inversion method. A method for dynamically rescaling the coarse-grained simulations to accurately predict the viscoelastic stress relaxation function is developed by matching the atomistic and coarse-grained diffusion rates. Analysis shows that quantitative predictions of the stress relaxation response of a complicated polymer can be computed from such multiscale approaches with reasonable accuracy. In conclusion, several outstanding challenges in coarse-grained modeling of polymers and bridging such models with continuum models are presented.

Atom-to-continuum methods for gaining a fundamental understanding of fracture.

This report describes an Engineering Sciences Research Foundation (ESRF) project to characterize and understand fracture processes via molecular dynamics modeling and atom-to-continuum methods. Under this aegis we developed new theory and a number of novel techniques to describe the fracture process at the atomic scale. These developments ranged from a material-frame connection between molecular dynamics and continuum mechanics to an atomic level J integral. Each of the developments build upon each other and culminated in a cohesive zone model derived from atomic information and verified at the continuum scale. This report describes an Engineering Sciences Research Foundation (ESRF) project to characterize and understand fracture processes via molecular dynamics modeling and atom-to-continuum methods. The effort is predicated on the idea that processes and information at the atomic level are missing in engineering scale simulations of fracture, and, moreover, are necessary for these simulations to be predictive. In this project we developed considerable new theory and a number of novel techniques in order to describe the fracture process at the atomic scale. Chapter 2 gives a detailed account of the material-frame connection between molecular dynamics and continuum mechanics we constructed in order to best use atomic information from solid systems. With this framework, in Chapter 3, we were able to make a direct and elegant extension of the classical J down to simulations on the scale of nanometers with a discrete atomic lattice. The technique was applied to cracks and dislocations with equal success and displayed high fidelity with expectations from continuum theory. Then, as a prelude to extension of the atomic J to finite temperatures, we explored the quasi-harmonic models as efficient and accurate surrogates of atomic lattices undergoing thermo-elastic processes (Chapter 4). With this in hand, in Chapter 5 we provide evidence that, by using the appropriate energy potential, the atomic J integral we developed is calculable and accurate at finite/room temperatures. In Chapter 6, we return in part to the fundamental efforts to connect material behavior at the atomic scale to that of the continuum. In this chapter, we devise theory that predicts the onset of instability characteristic of fracture/failure via atomic simulation. In Chapters 7 and 8, we describe the culmination of the project in connecting atomic information to continuum modeling. In these chapters we show that cohesive zone models are: (a) derivable from molecular dynamics in a robust and systematic way, and (b) when used in the more efficient continuum-level finite element technique provide results that are comparable and well-correlated with the behavior at the atomic-scale. Moreover, we show that use of these same cohesive zone elements is feasible at scales very much larger than that of the lattice. Finally, in Chapter 9 we describe our work in developing the efficient non-reflecting boundary conditions necessary to perform transient fracture and shock simulation with molecular dynamics.