CABARET scheme for computational modelling of linear elastic deformation problems

A generalisation of the CABARET scheme for linear elasticity equations with accounting for plastic deformations is suggested in a Lagrangian framework. In accordance with the conservative characteristic decomposition CABARET method, conservation variables are defined in cell centres and 'active' flux variables are defined in cell faces. Linear elasticity equations, which correspond to the hyperbolic part of the problem, are solved in a strong conservation form to update the cell-centre variables in time at the predictor-corrector stages. Cell-face variables are updated in time using the characteristic decomposition along each of the characteristic directions. For plastic deformation, the classical Prandtl–Reuss model is used to restrict the deformation stress components in accordance with the elastic limit at each step of the scheme. The Lagrangian step includes update of the coordinates of vertices of each control volume, which are slowly varying in time. Validation examples of the new method are provided for several test problems including the hard sphere denting into an elastic medium, shell deformation under the blast wave loading, and a spherical seismic wave propagation from a point source. The solutions of the new method are compared with the reference solutions available in the literature based on the artificial viscosity approaches and also on the Discontinuous Galerkin approach. Scalability results of the new algorithm for massively parallel computations are provided.