Publications

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Stochastic modelling approaches are presented to capture random effects at multiple time and length scales. Random processes that occur at the microscale produce nondeterministic effects at the macroscale. Here we present three stochastic modeling approaches that describe random processes at microscopic length scales and map these processes to the macroscopic length scale. The first stochastic modeling approach is based upon a particle based numerical technique to solve a Stochastic Differential Equation (SDE) using an arbitrary diffusion process to capture random processes at the microstructural level. The second approach prescribes a Probability Density Function (PDF) for the drift and diffusion of the random variable derived using the forward and backward Kolmogorov equations. This method requires mean and drift evolution PDF transport equations. The third approach is the coupling of multiple random variables which are dependent on each other. The relationship of the PDFs and a coupling function, known as a copula, produces a Joint Probability Density Function (JPDF). These stochastic modeling approaches are implemented into a Multiple Component (MC) shock physics computational code and used to model statistical fracture and reactive flow applications.

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The use of S2 glass/SC15 epoxy woven fabric composite materials for blast and ballistic protection has been an area of on-going research over the past decade. In order to accurately model this material system within potential applications under extreme loading conditions, a well characterized and understood anisotropic equation of state (EOS) is needed. This work details both an experimental program and associated analytical modelling efforts which aim to provide better physical understanding of the anisotropic EOS behavior of this material. Experimental testing focused on planar shock impact tests loading the composite to peak pressures of 15 GPa in both the transverse and longitudinal orientations. Test results highlighted the anisotropic response of the material and provided a basis by which the associated numeric micromechanical investigation was compared. Results of the combined experimental and numerical modeling investigation provided insights into not only the constituent material influence on the composite response but also the importance of the plain weave microstructure geometry and the significance of the microstructural configuration.

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Recently the Lagrangian Material Point Method (MPM) [1] has been integrated into the Eulerian finite volume shock physics code CTH [2] at Sandia National Laboratories. CTH has the capabilities of adaptive mesh refinement (AMR), multiple materials and numerous material models for equation of state, strength, and failure. In order to parallelize the MPM in CTH two different approaches were tested. The first was a ghost particle concept, where the MPM particles are mirrored onto neighboring processors in order to correctly assemble the mesh boundary values on the grid. The second approach exchanges the summed mesh values at processor boundaries without the use of ghost particles. Both methods have distinct advantages for parallelization. These parallelization approaches were tested for both strong and weak scaling. This paper will compare the parallel scaling efficiency, and memory requirements of both approaches for parallelizing the MPM.

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The Lagrangian Material Point Method (MPM) [1, 2] has been implemented into the Eulerian shock physics code CTH [3] at Sandia National Laboratories. Eulerian hydrodynamic methods are useful for large deformation problems, where mesh tangling typically leads to difficulties for Lagrangian finite element methods. However, Eulerian techniques suffer from numerical diffusion due to advection, which can be problematic for many material models requiring the transport of a damage parameter or other state variables that need to remain sharp [4]. The inclusion of the MPM in CTH allows for the accurate simulation of structural response to shock loading in a single framework. This paper presents a comparison of the shock response of the MPM and CPDI to the CTH hydrodynamics code. © Published under licence by IOP Publishing Ltd.

Recently there has been renewed interest in the dynamic response of composite materials; specifically low density epoxy matrix binders strengthened with continuous reinforcing fibers. This is in part due to the widespread use of carbon fiber composites in military, commercial, industrial, and aerospace applications. The design community requires better understanding of these materials in order to make full use of their unique properties. Planar impact testing was performed resulting in pressures up to 15 GPa on a unidirectional carbon fiber - epoxy composite, engineered to have high uniformity and low porosity. Results illustrate the anisotropic nature of the response under shock loading. Along the fiber direction, a two-wave structure similar to typical elastic-plastic response is observed, however, when shocked transverse to the fibers, only a single bulk shock wave is detected. At higher pressures, the epoxy matrix dissociates resulting in a loss of anisotropy. Greater understanding of the mechanisms responsible for the observed response has been achieved through numerical modeling of the system at the micromechanical level using the CTH hydrocode. From the simulation results it is evident that the observed two-wave structure in the longitudinal fiber direction is the result of a fast moving elastic precursor wave traveling in the carbon fibers ahead of the bulk response in the epoxy resin. Similarly, in the transverse direction, results show a collapse of the resin component consistent with the experimental observation of a single shock wave traveling at speeds associated with bulk carbon. Experimental and simulation results will be discussed and used to show where additional mechanisms, not fully described by the currently used models, are present. © Published under licence by IOP Publishing Ltd.

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The Lagrangian Material Point Method (MPM) [1, 2] has been implemented into the Eulerian shock physics code CTH[3], at Sandia National Laboratories. Since the MPM uses a background grid to calculate gradients, the method can numerically fracture if an insufficient number of particles per cell are used in high strain problems. Numerical fracture happens when the particles become separated by more than a grid cell leading to a loss of communication between them. One solution to this problem is the Convected Particle Domain Interpolation (CPDI) technique[4] where the shape functions are allowed to stretch smoothly across multiple grid cells, which alleviates this issue but introduces difficulties for parallelization because the particle domains can become non-local. This paper presents an approach where the particles are dynamically split when the volumetric strain for a particle becomes greater than a set limit so that the particle domain is always local, and presents an application to a large strain problem.

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