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Discrete element and time-integration methods forelasto-plasticity and dynamic cracking

Abstract : The present Ph.D. dissertation proposes contributions to discrete element methods (DEM) and explicit time integration schemes with a view towards dynamic cracking for metallic materials under dynamic loading. DEM, which are usually used to simulate granular materials, are understood through the prism of gradient discretization methods in order to simulate continuous materials. The method has been extended from previous Voronoi meshes to support generalpolyhedral meshes. Material behaviours have been extended from elasto-dynamics to dynamic elasto-plasticity through the addition of a tensorial degree of freedom per mesh cell. The method is robust with respect to the incompressible limit and its parameters only depend on material parameters. Moreover, an explicit pseudo-energy conserving time integration method has been developed, even for nonlinear behaviours and variable time steps, so as to avoid thedissipation of energy available for plastic dissipation and cracking. The method has been coupled to the proposed DEM. Finally, Griffith crack propagation through the mesh facets has been adapted to the present DEM for linear elastic behaviours in two space dimensions. The energy release rate is computed for every cracking mode using the stress intensity factors approximated close to the crack. A criterion of maximization of elastic energy density is used tosimulate kinking
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Submitted on : Tuesday, August 18, 2020 - 10:16:09 AM
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Frédéric Marazzato. Discrete element and time-integration methods forelasto-plasticity and dynamic cracking. General Mathematics [math.GM]. Université Paris-Est, 2020. English. ⟨NNT : 2020PESC1001⟩. ⟨tel-02916866⟩

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