Inter-Element Stabilization for Linear Large-Deformation Elements to Solve Coupled CFD/CSD Blast and Impact Problems

摘要

In this work a stabilized large deformation element suitable for real coupled fluid/solid simulations is presented. The element uses a mixed interpolation (Q1/P0): Standard continuous tri-linear finite element (FE) functions for the kinematic variables (displacements, velocities and accelerations), and a constant pressure per element (piecewise discontinuous pressures). It is well known that this type of element may show spurious pressure modes (chessboard mode) when is used to approximate incompressible fields (i.e. plastic flow, incompressible fluids, etc,). The mathematical explanation for such a behavior is the element inability of fulfilling the BB condition (the element is not div-stable). However, in Codina et al., the P1/P0 element is stabilized by means of a variational multiscale method (VMS), and it is used to solve the Stokes problem (incompressible flow equations at very low Reynolds number). Following the ideas of the cited reference, the authors of this work added to the standard large-deformation Lagrangian FE (Galerkin) formulation, a stabilization contribution which is only evaluated over the inter-element boundaries. Such a term enforces in a weak manner the pressure continuity and, in that way, it adds control over the inter-element pressure jumps (in general this procedure may be used to stabilize elements with discontinuous pressures). The method is clearly consistent: At the continuous level the pressures are continuous and the new term enforces such continuity at the discrete level. The stabilized IEOSS-Q1/P0 solid element (Inter-Element Orthogonal Subgrid-Scale Stabilized Q1/P0 element) was embedded into an efficient FE scheme to deal with large deformation problems. Others main ingredients of the formulation are: Some phenomeno-logical material models (concrete, steel, sand, rock, etc,) to deal with damage and fracture of structures, a general contact algorithm which uses bin technology to perform the node-face searching operations in a very efficient manner, and a cracking procedure to deal with the topology changes due to crack propagation and fragment formation. All the schemes, contact included, have been fully parallelized and coupled using a loose-embedded procedure with the well-established CFD (computational fluid dynamics) code FEFLO. Several real 3D coupled CFD/CSD cases, two of them with experimental comparison, are presented to validate the scheme.