J. Burghardt, B. Leavy, J. Guilkey, Z. Xue, R. Brannon
The capability of the generalized interpolation material point (GIMP) method in simulation of penetration events is investigated. A series of experiments was performed wherein a shaped charge jet penetrates into a stack of aluminum plates. Electronic switches were used to measure the penetration time history. Flash x-ray techniques were used to measure the density,length, radius and velocity of the shaped charge jet. Simulations of the penetration event were performed using the Uintah MPM/GIMP code with several different models of the shaped charge jet being used. The predicted penetration time history for each jet model is compared with the experimentally observed penetration history. It was found that the characteristics of the predicted penetration were dependent on the way that the jet data are translated to a discrete description. The discrete jet descriptions were modified such that the predicted penetration histories fell very close to the range of the experimental data. In comparing the various discrete jet descriptions it was found that the cumulative kinetic energy flux curve represents an important way of characterizing the penetration characteristics of the jet. The GIMP method was found to be well suited for simulation of high rate penetration events.
In a conventional MPM formulation, the shape functions on the grid are the same as in a traditional FEM solution. In the CPDI, the shape functions on the grid are replaced by alternative (and still linearly complete*) shape functions, given by piecewise linear interpolations of the traditional FEM shape functions to the boundaries of the particles. This change provides FEM-level accuracy in moderately deforming regions while retaining the attractive feature of MPM that particles can move arbitrarily relative to one another in massively deforming regions (provided, of course, that the deformation is updated in a manner compatible with the constitutive model).
In the images below, the shaded regions are the traditional FEM “tent” linear shape functions in 1-D, and the solid lines are the CPDI interpolated shape functions, which clearly change based on particle position relative to the grid. Both the traditional FEM tent functions and these new CPDI functions are linearly complete (i.e., they can exactly fit any affine function). The tremendous advantage of CPDI is that the basis functions are extraordinarily simple over a particle domain, thus facilitating exact and efficient evaluation of integrals over particle domains.
The CSM group has independently confirmed a case study demonstrating the truth of a claim in the literature that any non-associative rate-independent model admits a non-physical dynamic achronistity instability. By stimulating a non-associative material in the “Sandler-Rubin wedge” (above yield but below the flow surface), plastic waves are generated that travel faster than elastic waves, thus introducing a negative net work in a closed strain cycle that essentially feeds energy into a propagating wave to produce unbounded increases in displacement with time.
Sandler-Rubin instability: an infinitesimal pulse grows as it propagates
The Uintah computational framework (UCF) has been adopted for simulation of shaped charge jet penetration and subsequent damage to geological formations. The Kayenta geomechanics model, as well as a simplified model for shakedown simulations has been incorporated within the UCF and is undergoing extensive development to enhance it to account for fluid in pore space.
A generic penetration simulation using Uintah
The host code (Uintah) itself has been enhanced to accommodate material variability and scale effects. Simulations have been performed that import flash X-ray data for the velocity and geometry of a particulated metallic jet so that uncertainty about the jet can be reduced to develop predictive models for target response. Uintah’s analytical polar decomposition has been replaced with an iterative algorithm to dramatically improve accuracy under large deformations. Continue reading