Paul T. Giguere

Material point method enhanced by modified gradient of shape function

A numerical scheme of computing quantities involving gradients of shape functions is introduced for the material point method (MPM), so that the quantities are continuous as material points move across cell boundaries. The noise and instability caused by cell crossing of the material points are then eliminated. In this scheme, the formulas used to compute these quantities can be expressed in the same forms as in the original material point method, but with the gradient of the shape function modified. For one-dimensional cases, the gradient of the shape function used in the generalized interpolation material point (GIMP) method is a special case of the modified gradient if the characteristic function of a material point is introduced. The characteristic function of a material point is not otherwise needed in this scheme, therefore difficulties in tracking its evolution are avoided. Although the support of the modified gradient of a shape function is enlarged from the cell containing the material point to also include the immediate neighbor cells, all the non-local effects of a material point can be accounted for by two consecutive local operations. Therefore this scheme can be used in calculations with unstructured grids. This scheme is proved to satisfy mass and momentum conservations exactly. The error in energy conservation is shown to be second order on both spatial and temporal discretizations. Although the error in energy conservation is the same order as that in the original material point method, numerical examples show that this scheme has significantly better energy conservation properties than those of the original material point method.

Distribution coefficient algorithm for small mass nodes in material point method

When using the time explicit material point method to simulate interaction of materials accompanied by large deformations and fragmentation, one often encounters a numerical instability caused by small node mass, because acceleration on a mesh node is obtained by dividing the total force on the node by the mass of the node. When the material points are in the far sides of the cells containing the node, typically happening near material interfaces, the node mass can be very small leading to artificially large acceleration and then numerical instability. For the case of small material deformations, this instability is typically avoided by placing the material points away from cell boundaries. For cases with large deformations, with the exception of initial conditions, there is no control on locations of the material points. The instability caused by small mass nodes is often encountered. To avoid this instability tiny time steps are usually required in a numerical calculation. In this work, we present a numerical algorithm to treat this instability. We show that this algorithm satisfies mass and momentum conservation laws. The error in energy conservation is proportional to the second order of the time step, consistent with the explicit material point method. Numerical implementation of the algorithm is described. Numerical examples show effectiveness of the algorithm.

AN APPROACH TO FLUID MECHANICS CALCULATIONS ON SERIAL AND PARALLEL COMPUTER ARCHITECTURES

SUMMARY The T ransient R eactor A nalysis C ode (TRAC) is a large FORTRAN thermal-hydraulics program designed to solve problems involving internal flows in nuclear reactors. The current versions have been designed for a CDC 7600 and CRAY 1 but benchmarks have been run in parallel simulations. This paper will discuss the methods in use, the reason that these techniques are effective, and their extension to parallel machines.

NSR&D FY14 Final Report: Friction/Impact Modeling

The LANL-developed CartaBlanca code uses advanced techniques, including the Dual Domain Material Point (DDMP) method, to calculate fluid, solid motions and fluid-structure interactions. In the last year we have implemented the ViscoSCRAM material model in CartaBlanca based on Clements’ Abaqus-Explicit Finite Element implementation. In this fiscal year, we study numerical properties of this implementation. To consider coupled mechanical, thermal and chemical effects, we have implemented Henson’s HE decomposition model to couple with the thermal and mechanical packages in CartaBlanca. We have also developed porous media flow modules to consider heat convection effects of the reaction product gas inside pores of HE. The next immediate step is to perform numerical simulations to study interactions among these different mechanisms. We have started such calculation and obtained interesting initial results at the end of this fiscal year.