A long-standing area of research for Eulerian shock wave physics codes has been the treatment of strength and damage for materials. Here we present a method that will aid in the analysis of strength and failure in shock physics applications where excessive diffusion of critical variables can occur and control the solution outcome. Eulerian methods excel for large deformation simulations in general but are inaccurate in capturing structural behavior. Lagrangian methods provide better structural response, but finite element meshes can become tangled. Therefore, a technique for merging Lagrangian and Eulerian treatments of material response, within a single numerical framework, was implemented in the Multiple Component computational shock physics hydrocode. The capability is a Lagrangian/Eulerian Particle Method (LEPM) that uses particles to interface a Lagrangian treatment of material strength with a more traditional Eulerian treatment of the Equation of State (EOS). Lagrangian numerical methods avoid the advection diffusion found in Eulerian methods, which typically strongly affects strength constitutive law internal variables, such as equivalent plastic strain, porosity and/or damage. The Lagrangian capability enhances existing capabilities and permits accurate predictions of high rate, large deformation and/or shock of mechanical structures.
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.
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.
11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014
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.
Particle-Based Methods III: Fundamentals and Applications - Proceedings of the 3rd International Conference on Particle-based MethodsFundamentals and Applications, Particles 2013
The dynamic failure of materials in a finite volume shock physics computational code poses many challenges. Sandia National Laboratories has added Lagrangian markers as a new capability to CTH. The failure process of a marker in CTH is driven by the nature of Lagrangian numerical methods. This process is performed in three steps and the first step is to detect failure using the material constitutive model. The constitutive model detects failure computing damage or other means from the strain rate, strain, stress, etc. Once failure has been determined the material stress and energy states are released along a path driven by the constitutive model. Once the magnitude of the stress reaches a critical value, the material is switched to another material that behaves hydrodynamically. The hydrodynamic failed material is by definition non-shear-supporting but still retains the Equation of State (EOS) portion of the constitutive model. The material switching process is conservative in mass, momentum and energy. The failed marker material is allowed to fail using the CTH method of void insertion as necessary during the computation.
Particle-Based Methods III: Fundamentals and Applications - Proceedings of the 3rd International Conference on Particle-based MethodsFundamentals and Applications, Particles 2013
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.