On some thermally coupled systems in solid mechanics across various time scales
Sur quelques systèmes couplés thermiquement en mécanique des solides à différentes échelles de temps
Résumé
The analysis of coupled thermo-mechanical phenomena in solid media is a scientific topic as old as it still presents as many new challenges. Motivated by practical engineering applications that are still evolving, such as mastering dynamic forming processes or the use of electric batteries, these analyzes may require the design of new modelings, and relevant numerical methods, built on the basis of a robust theoretical framework, and taking advantage of the specificities of each of the coupled physics. The research work presented in the context of this Habilitation to Supervise Research concerns some recent contributions in this field, in particular for phenomena occurring at various time scales.
Initially, we are interested in mechanical processes which are rather slow, coupled with transient diffusion. Continuous and incremental variational approaches have proven to be particularly fruitful and efficient for the modeling and numerical resolution of these coupled physics. These approaches have been used in the case of heat diffusion for problems involving large irreversible transformations, taking advantage in particular of the alternating adaptation of the computational meshes, as for the diffusion of chemical species possibly coupled with electrostatics for applications related to electrical batteries. For problems of transient diffusion of species in materials with complex microstructure, multi-scale transient homogenization approaches are relevant. We then present one way among others to build reduced models of numerical homogenization, drastically reducing the computational costs compared to more traditional approaches.
In a second step, we are interested in fast thermo-mechanical processes. High pulsed power technologies represent one means among others of exploiting these velocity effects, which permit for example to achieve certain metallic assemblies or to reach levels of deformation that the quasi-static domain does not allow. Some applications around the electromagnetic technology are shown, such as electromagnetic flanging or the disassembly of heterogeneous two-layer structures. In addition, the numerical simulation of impacts on structures can take advantage of so-called conservative formulations, more widespread in computational fluid dynamics, which allow in solid mechanics to unify in the same well-defined mathematical framework the formulations implemented in the codes dedicated to structural mechanics and hydro-codes. The thermodynamic consistency of the approach is supplemented by a description of the dissipative thermo-mechanical constitutive response formulated by a variational approach, and an associated discrete integrator driven by the internal energy density. Finally, to simulate fast dynamics problems involving large transformations, a conservative Lagrangian numerical method based on material points is proposed and allows to build non-oscillatory high-order approximations for the numerical resolution of this conservative formulation.
The proposed research project is based (without being exhaustive) on the more advanced development of the proposed approaches in terms of modeling, numerical methods and assembly or disassembly processes; on the coupling of mechanics with other physics like electromagnetism; on the construction of equivalent simplified models.
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