An artificial-viscosity method for the lagrangian analysis of shocks in solids with strength on unstructured, arbitrary-order tetrahedral meshes

We present an artificial viscosity scheme tailored to finite-deformation Lagrangian calculations of shocks in materials with or without strength on unstructured tetrahedral meshes of arbitrary order. The artificial viscous stresses are deviatoric and satisfy material-frame indifference exactly. We have assessed the performance of the method on selected tests, including: a two-dimensional shock tube problem on an ideal gas; a two-dimensional piston problem on tantalum without strength; and a three-dimensional plate impact problem on tantalum with strength. In all cases, the artificial viscosity scheme returns stable and ostensibly oscillation-free solutions on meshes which greatly underresolve the actual shock thickness. The scheme typically spreads the shock over 4 to 6 elements and captures accurately the shock velocities and jump conditions.

[1]  R. D. Richtmyer,et al.  A Method for the Numerical Calculation of Hydrodynamic Shocks , 1950 .

[2]  J. Bogdanoff,et al.  On the Theory of Dislocations , 1950 .

[3]  P. Lax,et al.  Systems of conservation laws , 1960 .

[4]  William D. Schulz.  Tensor Artificial Viscosity for Numerical Hydrodynamics , 1964 .

[5]  J. Lubliner.  On the thermodynamic foundations of non-linear solid mechanics , 1972 .

[6]  P. G. Ciarlet,et al.  Numerical analysis of the finite element method , 1976 .

[7]  Mark L. Wilkins,et al.  Use of artificial viscosity in multidimensional fluid dynamic calculations , 1980 .

[8]  D. Steinberg,et al.  A constitutive model for metals applicable at high-strain rate , 1980 .

[9]  P. Woodward,et al.  The numerical simulation of two-dimensional fluid flow with strong shocks , 1984 .

[10]  T. Belytschko,et al.  Computational Methods for Transient Analysis , 1985 .

[11]  W. F. Noh.  Errors for calculations of strong shocks using an artificial viscosity and artificial heat flux , 1985 .

[12]  J. W. Swegle,et al.  Shock viscosity and the prediction of shock wave rise times , 1985 .

[13]  D. Benson.  Computational methods in Lagrangian and Eulerian hydrocodes , 1992 .

[14]  Anomalous physical effects from artificial numerical length scales , 1995 .

[15]  Michael Ortiz,et al.  Error estimation and adaptive meshing in strongly nonlinear dynamic problems , 1999 .

[16]  Ramon Codina,et al.  Shock capturing viscosities for the general fluid mechanics algorithm , 1998 .

[17]  M. Ortiz,et al.  The variational formulation of viscoplastic constitutive updates , 1999 .

[18]  Timothy J. Barth,et al.  High-order methods for computational physics , 1999 .

[19]  J. Marsden,et al.  Variational Integrators and the Newmark Algorithm for Conservative and Dissipative Mechanical Systems , 2000 .

[20]  Ronald E. Cohen,et al.  Thermal equation of state of tantalum , 2001 .