Application of the implicit TENSOR code to studies of containment of undergound nuclear tests

The TENSOR code, a two-dimensional finite-difference code, has been used extensively for the solution of stress wave propagation problems in materials, particularly those associated with the containment of underground nuclear test. These problems are typically characterized by shock waves at early times and by nearly incompressible flow at later times. To address this type of problem more economically, an implicit Newmark time integration has been implemented. Implicit differencing requires the solution of a coupled system of equations, by either direct or interative methods. An iterative technique has been selected to reduce the impact of the algorithm on the code structure and because it is the more economical method when only modest increases in timestep are desired. Although the algorithm is similar in some respects to the ICE method of Harlow and Amsden, substantial differences are required by the involvement of a complete stress tensor (instead of a scalar pressure) and by the highly nonlinear nature of the earth material constitutive relations