Toughness of soft materials such as elastomers and gels depends on their ability to dissipate energy and to reduce stress concentration at the crack tip. The primary energy dissipation mechanism is viscoelasticity. Most analyses and models of fracture are based on linear viscoelastic theory (LVT) where strains are assumed to be small and the relaxation mechanisms are independent of stress or strain history. A well-known paradox is that the size of the dissipative zone predicted by LVT is unrealistically small. Here we use a physically based nonlinear viscoelastic model to illustrate why the linear theory breaks down. Using this nonlinear model and analogs of crack problems, we give a plausible resolution to this paradox. In our model, viscoelasticity arises from the breaking and healing of physical cross-links in the polymer network. When the deformation is small, the kinetics of bond breaking and healing are independent of the strain/stress history and the model reduces to the standard linear theory. For large deformations, localized bond breaking damages the material near the crack tip, reducing stress concentration and dissipating energy at the same time. The damage zone size is a new length scale which depends on the strain required to accelerate bond breakingmore »
A network model of transient polymers: exploring the micromechanics of nonlinear viscoelasticity
Dynamic networks contain crosslinks that re-associate after disconnecting, imparting them with viscoelastic properties. While continuum approaches have been developed to analyze their mechanical response, these approaches can only describe their evolution in an average sense, omitting local, stochastic mechanisms that are critical to damage initiation or strain localization. To address these limitations, we introduce a discrete numerical model that mesoscopically coarse-grains the individual constituents of a dynamic network to predict its mechanical and topological evolution. Each constituent consists of a set of flexible chains that are permanently cross-linked at one end and contain reversible binding sites at their free ends. We incorporate nonlinear force–extension of individual chains via a Langevin model, slip-bond dissociation through Eyring's model, and spatiotemporally-dependent bond attachment based on scaling theory. Applying incompressible, uniaxial tension to representative volume elements at a range of constant strain rates and network connectivities, we then compare the mechanical response of these networks to that predicted by the transient network theory. Ultimately, we find that the idealized continuum approach remains suitable for networks with high chain concentrations when deformed at low strain rates, yet the mesoscale model proves necessary for the exploration of localized stochastic events, such as variability of the bond more »
- Award ID(s):
- 1761918
- Publication Date:
- NSF-PAR ID:
- 10295769
- Journal Name:
- Soft Matter
- ISSN:
- 1744-683X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Publisher's Version of Record
- https://doi.org/10.1039/D1SM00753J
