Using a simple one-dimensional shock problem as an example, the present paper investigates numerical properties of the original material point method (MPM), the generalized interpolation material point (GIMP) method, the convected particle domain interpolation (CPDI) method, and the dual domain material point (DDMP) method. For a weak isothermal shock of ideal gas, the MPM cannot be used with accuracy. With a small number of particles per cell, GIMP and CPDI produce reasonable results. However, as the number of particles increases the methods fail to converge and produce pressure spikes. The DDMP method behaves in an opposite way. With a small number of particles per cell, DDMP results are unsatisfactory. As the number of particles increases, the DDMP results converge to correct solutions, but the large number of particles needed for convergence makes the method very expensive to use in these types of shock wave problems in two-or three-dimensional cases. The cause for producing the unsatisfactory DDMP results is identified. A simple improvement to the method is introduced by using sub-points. With this improvement, the DDMP method produces high quality numerical solutions with a very small number of particles. Although in the present paper, the numerical examples are one-dimensional, all derivations are for multidimensional problems. With the technique of approximately tracking particle domains of CPDI, the extension of this sub-point method to multidimensional problems is straightforward. This new method preserves the conservation properties of the

No abstract

In this work we combine the dual domain material point method with molecular dynamics in an attempt to create a multiscale numerical method to simulate materials undergoing large deformations with high strain rates. In these types of problems, the material is often in a thermodynamically nonequilibrium state, and conventional constitutive relations or equations of state are often not available. In this method, the closure quantities, such as stress, at each material point are calculated from a molecular dynamics simulation of a group of atoms surrounding the material point. Rather than restricting the multiscale simulation in a small spatial region, such as phase interfaces, or crack tips, this multiscale method can be used to consider nonequilibrium thermodynamic effects in a macroscopic domain. This method takes the advantage that the material points only communicate with mesh nodes, not among themselves; therefore molecular dynamics simulations for material points can be performed independently in parallel. The dual domain material point method is chosen for this multiscale method because it can be used in history dependent problems with large deformation without generating numerical noise as material points move across cells, and also because of its convergence and conservation properties.

Multi-scale calculation based on dual domain material point method combined with molecular dynamics by Tilak R. Dhakal This dissertation combines the dual domain material point method (DDMP) with molecular dynamics (MD) in an attempt to create a multi-scale numerical method to simulate materials undergoing large deformations with high strain rates. In these types of problems, the material is often in a thermodynamically non-equilibrium state, and conventional constitutive relations are often not available. In this method, the closure quantities, such as stress, at each material point are calculated from a MD simulation of a group of atoms surrounding the material point. Rather than restricting I would like to thank Physics and

No abstract