A finite strain viscoelastic model with damage and tension/compression asymmetry

In an effort to bring some clarification on the vast literature on finite strain viscoelastic models, initially defined for elastomers, a review of the pioneering models on finite strain viscoelastic from Le Tallec et al. (1993), Lion (1997) and Reese and Govindjee (1998) has shown that these models are totally equivalent [1]. It is not easy to see it at first sight since these models are written in the reference, intermediate and current configurations.  Actually, all other models from the literature are similar and unified into a general model. 
Written in a classic generalized Maxwell scheme, the viscosities may be chosen constant, or dependent on the strain and/or strain rate. We have proposed an analysis on the interest and drawbacks of considering one non-constant viscosity in comparison with several constant viscosities [1]. 

The general model viscoelastic model is the first part in the definition of a continuum mechanics model, thermodynamically consistent, and proposing all the features of behavior displayed by solid propellants. By adding to it, i) a temperature dependence based on the time-temperature superposition principle, property displayed by the amorphous binder, ii) damage due to the binder debonding from the energetic fillers upon mechanical loading, iii) and tension/compression asymmetry due to the high amount of fillers, one may define a complete model appropriate to well reproduce propellant data from the literature[2]. The constitutive equations have been implemented in Abaqus finite element codes for further calculations of propellant loading.

This work is part of Florian Gouhier’s PhD.
[1]F. Gouhier, J. Diani, 2024. A comparison of finite strain viscoelastic models based on the multiplicative decomposition.European Journal Mechanics of Solids A, 108, 105424, https://doi.org/10.1016/j.euromechsol.2024.105424.
[2] A finite strain viscoelastic model with damage and tension-compression asymmetry considerations for solid propellants. Mechanics of Materials, 199, 105152, https://doi.org/10.1016/j.mechmat.2024.105152.