  Most research on the simulation of deformation and failure of metals has been
and continues to be performed using the finite element method. However, the
issues of mesh entanglement under large deformation, considerable complexity in
handling contact, and difficulties encountered while solving large deformation
fluid-structure interaction problems have led to the exploration of alternative
approaches. The material point method uses Lagrangian solid particles embedded
in an Eulerian grid. Particles interact via the grid with other particles in
the same body, with other solid bodies, and with fluids. Thus, the three issues
mentioned in the context of finite element analysis are circumvented.
  In this paper, we present simulations of cylinders which fragment due to
explosively expanding gases generated by reactions in a high energy material
contained inside. The material point method is the numerical method chosen for
these simulations discussed in this paper. The plastic deformation of metals is
simulated using a hypoelastic-plastic stress update with radial return that
assumes an additive decomposition of the rate of deformation tensor. Various
plastic strain, plastic strain rate, and temperature dependent flow rules and
yield conditions are investigated. Failure at individual material points is
determined using porosity, damage and bifurcation conditions. Our models are
validated using data from high strain rate impact experiments. It is concluded
that the material point method possesses great potential for simulating high
strain-rate, large deformation fluid-structure interaction problems.
