Solid Dynamics

VTF simulations of the ballistic impact (top) and penetration (bottom) of a steel plate

One immediate challenge for the new center is to formulate physics-based, multiscale, validated models of material behavior that are well-suited to the new overarching application. In particular, we shall require material models that are sufficiently fast to allow for the extensive certification-driven computational campaign envisioned under the PSAAP Center. Such computational campaign calls for extensive parametric studies involving large numbers of runs, as opposed to a few isolated ‘hero’ calculations. In order to obtain models of the requisite numerical efficiency, we shall make extensive use of the tools and principles of multiscale mathematics. In particular, we shall seek to derive explicit models of effective behavior at all length scales, thus bypassing the need for expensive ‘on-the-fly’ calculations of microstructure. We shall collectively refer to such material models as ‘Fast Multiscale Models’. Another key challenge faced by the center is the extension of material models to higher pressures and temperatures characteristic of hypervelocity impact, and the simulation of plasma states occurring during the initial impact flash.

The Solid Dynamics group will also develop Lagrangian capability for the simulation of hypervelocity impact to be used as part of the Uncertainty Quantification calculations. Ballistic impact can be simulated using fully-Lagrangian finite-element methodology such as presently available in the Cetern’s Virtual Testing Facility (VTF). An extensive Lagrangian methodology has been developed by Caltech’s ASC/ASAP Center, including: composite finite elements specially designed for finite-deformation plasticity and ballistic impact dynamic conditions; cohesive elements for simulating brittle fracture and fragmentation; shear-band and spall elements; thermo-mechanical coupling; graph-based parallel fracture and fragmentation; variational integrators; variational r and h-adaption; variational contact and friction; and a suite of multiscale material models. This capability will provide the basis for simulations of the integrated experiment IE1 planned for year 1.

Lagrangian particle methods such Smoothed Particle Hydrodynamics (SPH) and the Material Point Method (MPM) are attractive for simulations of hypervelocity impact. Despite their many attractive features, these methods are known to suffer from major shortcomings, most notably, difficulty in enforcing boundary conditions, contact conditions and numerical instabilities in tension. Numerous attempts at overcoming these deficiencies have been based on sundry extensions and modifications of the kernel functions and their derivatives, the introduction of additional stress points, and others. While some improvements have been reported based on these methods, they nevertheless add greatly to the cost of the method and fail to remove the essential difficulties entirely. We will continue to develop meshless approaches based on information-theoretical principles such as maximum entropy (max-ent) estimation that overcome the essential difficulties of particle methods. We will combine the max-ent approach with material point methodology to develop max-ent material point (MEMP) methods that are stable, monotone across shocks, convergent and that satisfy exactly all conservation laws. These MEMP methods will provide one of the core VTF capabilities for the simulation hypervelocity impact.