The second-order Godunov method is extended to dynamic wave propagation in two-dimensional solids undergoing nonlinear finite deformation. It is shown that this explicit method is linearly stable for timesteps satisfying the standard CFL condition, does not support the development of hourglass modes, and handles non-reflecting boundaries very naturally. The computational cost is essentially one evaluation of the kinetic equation of state per cell and timestep, the same as explicit finite element methods employing reduced quadrature. © 1994 Springer-Verlag.
Solids;Mechanics;Wave transmission;Deformation;Equations of motion;Convergence of numerical methods;Finite element method;Approximation theory;Computational complexity;Equations of state;