Publications

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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.

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.

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.

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