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A Computational Framework for a first-order system of conservation laws in thermoelasticity

Abstract : It is evidently not trivial to analytically solve practical engineering problems due to their inherent nonlinearities. Moreover, experimental testing can be extremely costly and time-consuming. In the past few decades, therefore, numerical techniques have been progressively developed and utilised in order to investigate complex engineering applications through computer simulations. In the context of fast thermo-elastodynamics, modern commercial packages are typically developed on the basis of second order displacement-based finite element formulations and, unfortunately, that introduces a series of numerical shortcomings (e.g. detrimental locking, hour-glass modes, spurious pressure oscillations). To rectify these drawbacks, a mixed-based set of first order hyperbolic conservation laws for thermo- elastodynamics is presented in terms of the linear momentum per unit undeformed volume, the deformation gradient, its co-factor, its Jacobian and the balance of total Energy. Interestingly, the conservation formulation framework allows exploiting available CFD techniques in the context of solid dynamics. From a computational standpoint, two distinct spatial discretisations are employed, namely, Vertex-Centred Finite Volume Method (VCFVM) and Smooth Particle Hydrodynamics (SPH). A linear reconstruction procedure together with a slope limiter is employed in order to ensure second order accuracy in space whilst avoiding numerical oscillations in the vicinity of sharp gradients. The semi-discrete system of equations is then temporally discretised using a second-order Total Variation Diminishing (TVD) Runge-Kutta time integrator. Finally, a wide spectrum of challenging examples is presented in order to assess both the performance and applicability of the proposed schemes. The new formulation is proven to be very efficient in nearly incompressible thermoelasticity in comparison with classical finite element displacement-based approaches.
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Submitted on : Tuesday, June 15, 2021 - 6:34:10 PM
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Ataollah Ghavamian. A Computational Framework for a first-order system of conservation laws in thermoelasticity. Mechanics of materials [physics.class-ph]. École centrale de Nantes; University of Swansea (Swansea (GB)), 2020. English. ⟨NNT : 2020ECDN0004⟩. ⟨tel-03261606⟩

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