Eulerian methods for solids, solid/fluid interaction, and moving interfaces

Study of compressible solid/fluid interfaces - Development of improved Level Set methods for moving interfaces

We have developed a three-dimensional Eulerian method for simulating dynamic systems comprising multiple compressible solid and fluid components where internal boundaries are tracked using level-set functions. Aside from the interface interaction calculation within mixed cells, each material is treated independently and the governing constitutive laws solved using a conservative finite volume discretisation based upon the solution of Riemann problems to determine the numerical fluxes. The required reconstruction of mixed cell volume fractions and cut cell geometries is presented in detail using the level-set fields. High-order accuracy is achieved by incorporating the weighted-essentially non-oscillatory (WENO) method and RungeKutta time integration. A model for elastoplastic solid dynamics is employed formulated using the tensor of elastic deformation gradients permitting the equations to be written in divergence form. The scheme has been validated using selected one-dimensional initial value problems for which exact solutions are derived, a two-dimensional void collapse, and a three-dimensional simulation of a confined explosion.

Pressure contours at the indicated times for the confined explosion example. Only those cells that contain either solid or fluid material are shown in order to highlight the geometries

High velocity impact - Dynamic friction

Friction occurring at the interface between dissimilar metallic components as a result of high velocity impact or explosive loading can have a profound effect on the subsequent motion. A comprehensive understanding of the involved processes across a wide range of initial conditions remains outstanding. Dry sliding of single crystal silver on copper at high pressure is investigated for a range of sliding speeds using a multi-scale modelling method based upon the domain decomposition approach (molecular dynamics in the near interface region and continuum mechanics elsewhere). The transient solutions reveal detailed observations of the processes that lead to phenomena such as the growth of epitaxial layers of the softer material, shifting of the sliding interface due to formation of shear-bands, development of amorphous structures, and ultimately the resultant motion of the components. Analysis of the results also links these processes to the changes in the state of the material through growth of dislocations and thermal effects.

Sliding material interfaces due to shock wave impact (top). The atomistic domain (bottom) showing atoms coloured by the centro-symmetric parameter, for a sliding speed of v=400 m/s. From left-to-right, the respective time instants are: t=27 ps, t=81 ps, t=135 ps, t=189 ps, t=243 ps, t=297 ps, t=351 ps.

References

  • P. Barton, B. Obadia, D. Drikakis, A conservative level-set based method for compressible solid/fluid problems on fixed grids, Journal of Computational Physics, Vol 230, Issue 21, 2011, 7867-7890, 2011.
  • P.T. Barton, M. Kalweit, D. Drikakis, G. Ball, Multi-scale analysis of high-speed dynamic friction, Journal of Applied Physics, 110(9), 093520, 2011
  • P. Barton, D. Drikakis, An Eulerian method for multi-component problems in non-linear elasticity with sliding interfaces, Journal of Computational Physics, Vol. 229, Issue 15, 1, 5518-5540, 2010.
  • P. T. Barton, D. Drikakis, E. I. Romenski, An Eulerian finite-volume scheme for large elastoplastic deformations in solids, International Journal for Numerical Methods in Engineering, Vol. 81, Issue 4, 453-484, 2010.
  • P. T. Barton, D. Drikakis, E.I. Romenski, V. Titarev, Exact and approximate solutions of Riemann problems in non-linear elasticity, Journal of Computational Physics, Vol. 228, 18, 7046-7068, 2009.