Concurrent two-scale model for the viscoelastic behavior of elastomers filled with hard nanoparticles

Abstract

A dynamic two-scale model is developed for describing the mechanical behavior of elastomers filled with hard nanoparticles. Using nonequilibrium thermodynamics, a closed system of evolution equations is derived, coupling continuum mechanics with a fine-scale description on the level of filler particles. So doing, a constitutive stress-strain relation emerges that is applicable to transient situations. In addition to the number density of filler particles, the particle arrangement is captured by the distribution of the difference vector between two representative interacting particles, which makes this model efficient in comparison with manyparticle models. The two-particle model presented here is analyzed numerically in oscillatory deformation, for two purposes. First, the nonlinearity of the model is studied in detail, in terms of the Payne effect, that compares favorably with the literature. And second, the two-particle model is compared with a corresponding many-particle model in the literature.

Two-scale model for the effect of physical aging in elastomers filled with hard nanoparticles

“…as done in [15][16][17][18]. Second, the lessons learned from that latter work can be built into the two-scale nanocomposite model developed in [5], which is the topic of this paper.…”

“…by NMR studies [2] or more recently by a mechanical analysis of model systems [3,4]. For more details on this issue, the reader is referred to, e.g., [5] and references therein.…”

“…Specific features of bulk polymer glasses that are relevant also for the glassy-bridge induced effects are the viscoplastic yielding behavior and strain softening, as well as the effect of physical aging on the mechanical behavior. For example, when making use of bulk yielding kinetics in the nanocomposite context, one can rationalize the highly nonlinear rate-dependent mechanical response of such nanocomposites, including the prominent Payne effect [5,[8][9][10].…”

“…In an earlier publication, a thermodynamically-inspired concurrent two-scale model has been developed to describe the mechanical behavior of elastomers filled with hard nanoparticles [5]. While that model takes the yielding kinetics of the glassy bridges into account, the physical aging of the glassy bridges is neglected.…”

Formulation of strongly non-local, non-isothermal dynamics for heterogeneous solids based on the GENERIC with application to phase-field modeling

“…This latter approach is closely related to the bracket formalism (Beris and Edwards 1994). Originally developed for complex fluids, the GENERIC-based approach has more recently been applied to the formulation of thermodynamic models (Hütter and Tervoort 2008b, c, d;Mielke 2011;Hütter and Svendsen 2011;2012;Hütter and van Breemen 2012;Hütter and Svendsen 2013;Gladkov et al 2016;Semkiv et al 2017) for elastic and inelastic solids. Recently, a non-isothermal phase-field model for alloy solidification was formulated based on the bracket formalism (Bollada et al 2017).…”