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This article is cited in 2 scientific papers (total in 2 papers)
CABARET scheme for computational modelling of linear elastic deformation problems
M. A. Zaitseva, S. A. Karabasovb a Nuclear Safety Institute, Moscow
b Queen Mary University of London
Abstract:
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.
Keywords:
elastic-plastic solid, deformation, modeling, parallel computation, CABARET scheme.
Received: 14.11.2016
Citation:
M. A. Zaitsev, S. A. Karabasov, “CABARET scheme for computational modelling of linear elastic deformation problems”, Matem. Mod., 29:11 (2017), 53–70
Linking options:
https://www.mathnet.ru/eng/mm3907 https://www.mathnet.ru/eng/mm/v29/i11/p53
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Abstract page: | 322 | Full-text PDF : | 104 | References: | 52 | First page: | 15 |
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