On the isogeometric approach for coupled thermomechanical problems at large strain

Lei Zhang (1) , Stéphane Lejeunes (1) , Dominique Eyheramendy (2)

1 LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]
2 M&S - Matériaux et Structures

In this contribution, we investigate isogeometric models for the simulation of dissipative elastomers under coupled thermomechanical loadings. We first study the question of convergence of an isogeometric temperature/displacement formulation in the case of thermoelasticity at small and large strains. In the context of nearly-incompressible behavior we adopt a mixed displacement/pressure/temperature formulation (e.g. [1]). We show that at least in the adiabatic and isothermal case we obtain a stable and convergent formulation that can be compared with other strategies (see for instance [2]). For the thermomechanical case, we discuss about the straightforward link between perturbed lagrangian variational principles and a thermodynamic approach based on the hybrid free energy. As shown in [3], this approach allows both for a better understanding and fitting of material parameters (isobaric heat capacity for instance) and is able to correctly describe free thermal expansion solution in the context of nearly incompressible behavior. From simple examples, we show that we can simply take into account entropic elasticity, thermal dilatation, viscous damping and self-heating phenomena in a mixed formulation and that we can qualitatively reproduce experimentally observed phenomena (see for instance figure 1). Références [1] Zhang, L. ; On an isogeometric approach for multi-fields coupled problems at finite strain ; PhD Thesis ; (2016) [2] Kadapa, C. and Dettmer, W. G. and Perić, D.; Subdivision based mixed methods for isogeometric ; Comput. Methods Appl. Mech. Eng., vol. 305, pp. 241–270, (2016) [3] Lion, A., and Dippel, B. and Liebl, C. ; Thermomechanical material modelling based on a hybrid free energy density depending on pressure, isochoric deformation and temperature.

Domaines: Mécanique [physics.med-ph]

Lei Zhang, Stéphane Lejeunes, Dominique Eyheramendy. On the isogeometric approach for coupled thermomechanical problems at large strain. Worshop on the Multiphysics Behavior of Rubber, Nov 2017, Marseille, France. pp.729 - 73. ⟨hal-01673972⟩