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Discontinuous Galerkin Modeling of Wave Propagation in Damaged Materials

Abstract : A discontinuous Galerkin (DG) technique for modeling wave propagation in damaged (brittle) materials is developed in this thesis. Two different types of mechanical models for describing the damaged materials are considered. In the first part of the thesis general micro-mechanics based damage models were used. A critical crack density parameter, which distinguishes between stable and unstable behaviors, wascomputed. A new DG-numerical scheme able to capture the instabilities and a micro-scale time step were proposed. An exact solution is constructed and the accuracy of the numerical scheme was analyzed. The wave propagation in one dimensional and anti-plane configuration was analyzed through several numerical computations. In the second part of the thesis the wave propagation in cracked materials with a nonlinear micro-structure (micro-cracks in frictional contact) was investigated. The numerical scheme developed makes use of a DG-method and an augmented Lagrangian technique. The effective wave velocity in a damaged material, obtained by a numerical upscaling homogenization method, was compared with analytical formula of effective elasticity theory. The wave propagation (speed, amplitude and pulse length) in micro-cracked materials in complex configurations was studied. Finally, numerical computations of blast wave propagation,for the both models, illustrate the role played by the micro-cracks orientation and by the friction.
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Submitted on : Wednesday, September 11, 2019 - 11:18:18 AM
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  • HAL Id : tel-02283789, version 1


Quriaky Gomez Carrero. Discontinuous Galerkin Modeling of Wave Propagation in Damaged Materials. Mechanics of materials [physics.class-ph]. Université Sorbonne Paris Cité, 2017. English. ⟨NNT : 2017USPCD054⟩. ⟨tel-02283789⟩



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