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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 breaking kinetics. These effects are illustrated by considering two cases with stress concentrations: the evolution of spherical damage in a viscoelastic body subjected to internal pressure, and a zero degree peel test.
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This content will become publicly available on June 1, 2026
Mechanics of CO2-induced dynamic covalent polymer networks: Constitutive modeling and crack healing
CO2-induced dynamic covalent polymer networks (DCPNs) have received significant attention due to their capability of sequestering CO2 to remodel material properties. Despite the promising success of carbon sequestration in the polymer, the mechanistic understanding of the CO2-induced polymer network is still at the very beginning. A theoretical framework to understand the CO2-induced formation of bulk networks and healing of interfacial cracks of DCPNs has not been established. Here, we build up a polymer-network-based theoretical model system that can mechanistically explain the constitutive behavior and crack healing of CO2-induced DCPNs. We assume that the DCPN consists of interpenetrating networks crosslinked by CO2-induced dynamic bonds which follow a force-dependent chemical kinetics. During the healing process, we consider the CO2 molecules diffuse from the surface to the crack interface to reform the polymer network for interfacial repair. Our theoretical framework can calculate the stress-strain behaviors of both original and healed DCPNs. We demonstrate that the theoretically calculated stress-strain responses of the original DCPNs across various CO2 concentrations, as well as those of healed DCPNs under different CO2 concentrations, consistently match the documented experimental results. We expect our model to become an invaluable tool for innovating, designing, understanding, and optimizing CO2-induced DCPNs.
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- Award ID(s):
- 1943598
- PAR ID:
- 10592460
- Publisher / Repository:
- Elsevier
- Date Published:
- Journal Name:
- Journal of the Mechanics and Physics of Solids
- Volume:
- 199
- Issue:
- C
- ISSN:
- 0022-5096
- Page Range / eLocation ID:
- 106098
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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