Contribution à l'homogénéisation des milieux viscoélastiques et introduction du couplage avec la température par extensions d'une approche incrémentale directe

Abstract : This study is devoted to the micromechanical modeling of viscoelastic composites using an incremental approach (IA) due to Lahellec and Suquet (2007). ln addition to be based on a rigorous thermodynamic framework, the IA allows solving the heterogeneous viscoelastic problem in the real time domain (i.e. without the Laplace transform). The first aim is to extend the IA application range in terms of local linear viscoelastic laws and microstructures. The second one is to attempt to introduce the coupling effects between the viscoelasticity and the temperature within the IA framework. First, the IA is coded in Python• and the program validated for simple viscoelastic laws, and for microstructures and loading paths already studied in Lahellec and Suquet (2007). The second part focuses on a theoretical generalization of the IA for many internal variables which are not necessarily deviatoric and for anisotropie phases. The resulting estlmates are progressively validated by confrontation to reference so lutions (full -field simulations) and especially the IA ability to deal with matrices described by generalized Maxwell laws (without and with volumetric anelastic strains). This part ends with a demonstration of the possible association of the IA with three linear homogenization schemes (Mori-Tanaka, Lielen's interpolation, scheme of Malekmohammadi et al. (2014)) in order to deal with various morphologies (fiber or part icle reinforced composites, wood strand-based composites). The last part focuses on the coupling between the viscoelasticity and the temperature within the IA framework. The initial and time discretized versions of the strongly coupled local problem are formulated. Then, increasing coupling levels are envisioned for a progressive approach of the solving procedure. The thermoelastic coupling, alone, is first studied (effect of the thermies on mechanics, without solving the heat equation). The resulting estimates for a periodic microstructure with elastic, thermoelastic then thermoviscoelastic fibers, in a thermoviscoelastic matrix are successfully compared to reference solutions. At last, the heat equation is simultaneously solved by taklng into account the viscoelastic dissipation within the matrix as a source term, in addition to the thermoelastic coupling term. The evolutions of the global temperature and response reveal relevant tendencies.
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Benjamin Tressou. Contribution à l'homogénéisation des milieux viscoélastiques et introduction du couplage avec la température par extensions d'une approche incrémentale directe. Autre. ISAE-ENSMA Ecole Nationale Supérieure de Mécanique et d'Aérotechique - Poitiers, 2016. Français. ⟨NNT : 2016ESMA0004⟩. ⟨tel-01327248⟩

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