Molecular simulation guided constitutive modeling on finite strain viscoelasticity of elastomers

Abstract

Viscoelasticity characterizes the most important mechanical behavior of elastomers. Understanding the viscoelasticity, especially finite strain viscoelasticity, of elastomers is the key for continuation of their dedicated use in industrial applications. In this work, we present a mechanistic and physics-based constitutive model to describe and design the finite strain viscoelastic behavior of elastomers. Mathematically, the viscoelasticity of elastomers has been decomposed into hyperelastic and viscous parts, which are attributed to the nonlinear deformation of the cross-linked polymer network and the diffusion of free chains, respectively. The hyperelastic deformation of a cross-linked polymer network is governed by the cross-linking density, the molecular weight of the polymer strands between cross-linkages, and the amount of entanglements between different chains, which we observe through large scale molecular dynamics (MD) simulations. Moreover, a recently developed non-affine network model [Davidson and Goulbourne, 2013, J. Mech. Phys. Solids, 61, 1784] is confirmed in the current work to be able to capture these key physical mechanisms using MD simulation. The energy dissipation during a loading and unloading process of elastomers is governed by the diffusion of free chains, which can be understood through their reptation dynamics. The viscous stress can be formulated using the classical tube model [Doi and Edwards, 1986, The theory of polymer dynamics, Clarendon Press, Oxford]; however, it cannot be used to capture the energy dissipation during finite deformation. By considering the tube deformation during this process, as observed from the MD simulations, we propose a modified tube model to account for the finite deformation behavior of free chains. Combing the non-affine network model for hyperelasticity and modified tube model for viscosity, both understood by molecular simulations, we develop a mechanism-based constitutive model for finite strain viscoelasticity of elastomers. All the parameters in the proposed constitutive model have physical meanings, which are signatures of polymer chemistry, physics or dynamics. Therefore, parametric materials design concepts can be easily gleaned from the model, which is also demonstrated in this study. The finite strain viscoelasticity obtained from our simulations agrees qualitatively with experimental data on both un-vulcanized and vulcanized rubbers, which captures the effects of cross-linking density, the molecular weight of the polymer chain and the strain rate.

Effect of Diphenyl Content on Viscoelasticity of Poly(dimethyl-co-diphenyl)siloxane Melt and Network

“…Interested readers can refer to eq 14 in our previous work. 39 Overall, our FEM framework is still capable of capturing the essential viscoelasticity of the siloxane copolymers.…”

“…In order to model the viscoelastic behavior of the copolymer, we adopted our previously reported FEM framework. 39 In this framework, it is assumed that the Cauchy stress (in tensor form) σ is decomposed into contributions from the elastic and viscous behaviors, as given in eq 3…”

“…The physical meaning of λ max is self-explanatory due to the limited stretchability of polymer chains. Following the literature, 39,40 we model the hyperelastic contribution to stress, i.e., σ E , by eq 4…”

“…Please refer to our previous work for more details. 39 In this study, model parameters (within eqs 4 and 5) were first optimized by fitting them to appropriate experimental characterization data. These optimized parameters were then fed to the FEM simulations to generate simulated stress−strain curves.…”

Predictive model for stress relaxation behavior of glassy polymers based on variable‐order fractional calculus

“…The basic phenological model was suggested by Eyring in 1936, demonstrating the rate and temperature dependence of the activated processes theoretically 12 . Afterward, several constitutive models were extended in order to simulate various loading experiments and to have broad applicability 13‐18 . For instance, Anand and Ames put forward a continuum constitutive model which indicates the salient features of the mechanical response of PMMA under different ambient temperatures with more than 20 parameters 19 .…”