Time dependent fracture of soft materials: linear versus nonlinear viscoelasticity

Unconstrained dynamic gel swelling generates transient surface deformations

Polymer gels are comprised of a three-dimensional, cross-linked network that can typically withstand the mechanical deformation associated with both swelling and de-swelling. Thus, gels can be designed with smart behaviors that require both stress generation and dissipation, making them well-suited to many applications including membrane technology, water capture devices, and drug delivery systems. In contrast to the fully swelled equilibrium state, limited research characterizes the unsteady-state swelling regime prior to equilibrium. It is in this regime where unique surface deformations can occur. Here we show how internal network constraints and external diffusive pressure can be leveraged to manipulate swelling kinetics and surface deformations in poly(ethylene glycol) gels during unconstrained, three-dimensional swelling. We find that increasing cross-linker molecular weight and swelling in ethanol, as opposed to water, are both effective routes to increase the time it takes to reach equilibrium but do so through different mechanisms. Networks with fewer internal constraints, manipulated via cross-linker chain-length, imbibe more solvent over a longer time. In contrast, swelling in ethanol reduces the amount of solvent imbibed by the network while increasing the time to reach equilibrium. Measurements of surface patterns during swelling establishes that an immediate, fast relaxation at the surface occurs during the first five minutes of swelling. However, the density and persistence of these features varies with solvent quality. These results establish a framework for how soft materials undergo dynamic deformation. Engineering transient surface properties while mitigating unwanted instabilities opens the door for emerging technologies such as smart anti-fouling and sensors.

BioTrojans: viscoelastic microvalve-based attacks in flow-based microfluidic biochips and their countermeasures

Flow-based microfluidic biochips (FMBs) are widely used in biomedical research and diagnostics. However, their security against potential material-level cyber-physical attacks remains inadequately explored, posing a significant future challenge. One of the main components, polydimethylsiloxane (PDMS) microvalves, is pivotal to FMBs' functionality. However, their fabrication, which involves thermal curing, makes them susceptible to chemical tampering-induced material degradation attacks. Here, we demonstrate one such material-based attack termed "BioTrojans," which are chemically tampered and optically stealthy microvalves that can be ruptured through low-frequency actuations. To chemically tamper with the microvalves, we altered the associated PDMS curing ratio. Attack demonstrations showed that BioTrojan valves with 30:1 and 50:1 curing ratios ruptured quickly under 2 Hz frequency actuations, while authentic microvalves with a 10:1 ratio remained intact even after being actuated at the same frequency for 2 days (345,600 cycles). Dynamic mechanical analyzer (DMA) results and associated finite element analysis revealed that a BioTrojan valve stores three orders of magnitude more mechanical energy than the authentic one, making it highly susceptible to low-frequency-induced ruptures. To counter BioTrojan attacks, we propose a security-by-design approach using smooth peripheral fillets to reduce stress concentration by over 50% and a spectral authentication method using fluorescent microvalves capable of effectively detecting BioTrojans.

Understanding the role of crosslink density and linear viscoelasticity on the shear failure of pressure-sensitive-adhesives

Pressure-sensitive-adhesives (PSAs) are ubiquitous in electronic, automobile, packaging, and biomedical applications due to their ability to stick to numerous surfaces without undergoing chemical reactions. Although these materials date back to the 1850s with the development of surgical tapes based on natural rubber, their resistance to shear loads remains challenging to predict from molecular design. This work investigates the role of crosslink density on the shear resistance of model PSAs based on poly(2-ethylhexyl acrylate-co-acrylic acid) physically crosslinked with aluminum acetylacetonate. The key result is that crosslinking PSAs leads to notable stress concentrations ahead of the peel front, as well as a transition from cohesive to adhesive failure. The shear stress distributions, as evaluated by means of a linearly viscoelastic shear lag model, suggest that this transition is related to the evolution of the ratio of the load transfer length to the bond length as dictated by the mechanical properties of the backing and adhesive layers, and the geometry of the tape.

Synthesis and Characterization of a Liquid Crystal-Modified Polydimethylsiloxane Rubber with Mechanical Adaptability Based on Chain Extension in the Process of Crosslinking

The mechanical adaptive material is a kind of functional material that can effectively dissipate energy and suppress the increase of its stress under continuous strain in a large deformation area, which are vital in artificial muscles, connection devices, soft artificial intelligence robots, and other areas. Scientists have been working to broaden the platform of the material's mechanical adaptive platform and improve its mechanical strength by specific structure design. Based on it, we expect to introduce a mechanism of energy dissipation from the molecular chain scale to further improve mechanical adaptability. We developed a liquid crystal-modified polydimethylsiloxane rubber with mechanical adaptability based on chain extension in the process of crosslinking. Results showed that liquid crystal (0.7 mol %)-modified silicone rubber can obviously dissipate energy to achieve mechanical adaptive function, and the energy dissipation ratio of polydimethylsiloxane rubber (MQ), 4-propyl-4'-vinyl-1,1'-bi(cyclohexane)-modified polydimethylsiloxane rubber (3CCV-MQ), and 4-methoxyphenyl-4-(3-butenyloxy) benzoate-modified polydimethylsiloxane rubber (MBB-MQ) gradually decreases from 30 to 24%. Excessive thiol groups of liquid crystal-modified polydimethylsiloxane react with its vinyl group to achieve the chain extension, which significantly improves the mechanical strength from 2.74 to 5.83 MPa and elongation at break from 733 to 1096%. This research offers some new insights into improving the mechanical strength of silicone rubber and is of great significance for the application of the mechanical adaptive material.

Physically motivated models of polymer networks with dynamic cross-links: comparative study and future outlook

Polymer networks consisting of a mixture of chemical and physical cross-links are known to exhibit complex time-dependent behaviour due to the kinetics of bond association and dissociation. In this article, we highlight and compare two recent physically based constitutive models that describe the nonlinear viscoelastic behaviour of such transient networks. These two models are developed independently by two groups of researchers using different mathematical formulations. Here, we show that this difference can be attributed to different viewpoints: Lagrangian versus Eulerian. We establish the equivalence of the two models under the special situation where chains obey Gaussian statistics and steady-state bond dynamics. We provide experimental data demonstrating that both models can accurately predict the time-dependent uniaxial behaviour of a poly(vinylalcohol) dual cross-link hydrogel. We review the advantages and disadvantages of both approaches in applications and close by discussing a list of open challenges and questions regarding the mathematical modelling of soft, viscoelastic networks.

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 kinetics, or the nucleation of micro-cavities that likely conceive damage and fracture.

Nonsteady fracture of transient networks: The case of vitrimer

We have discovered a peculiar form of fracture that occurs in polymer network formed by covalent adaptable bonds. Due to the dynamic feature of the bonds, fracture of this network is rate dependent, and the crack propagates in a highly nonsteady manner. These phenomena cannot be explained by the existing fracture theories, most of which are based on steady-state assumption. To explain these peculiar characteristics, we first revisit the fundamental difference between the transient network and the covalent network in which we highlighted the transient feature of the cracks. We extend the current fracture criterion for crack initiation to a time-evolution scheme that allows one to track the nonsteady propagation of a crack. Through a combined experimental modeling effort, we show that fracture in transient networks is governed by two parameters: the Weissenberg number [Formula: see text] that defines the history path of crack-driving force and an extension parameter Z that tells how far a crack can grow. We further use our understanding to explain the peculiar experimental observation. To further leverage on this understanding, we show that one can "program" a specimen's crack extension dynamics by tuning the loading history.

Force-dependent bond dissociation explains the rate-dependent fracture of vitrimers

We investigate the rate-dependent fracture of vitrimers by conducting a tear test. Based on the relationship between the fracture energy and the thickness of vitrimer films, we, for the first time, obtain the intrinsic fracture energy and bulk dissipation of vitrimers during crack extension. The intrinsic fracture energy strongly depends on tear speed, and such dependence can be well explained by Eyring theory. In contrast, the bulk dissipation only weakly depends on tear speed, which is drastically different from observations on traditional viscoelastic polymers. We ascribe such a weak rate-dependence to the strong force-sensitivity of the exchange reaction of the dynamic covalent bond in the vitrimer.

Gel rupture during dynamic swelling

Hydrogels have had a profound impact in the fields of tissue engineering, drug delivery, and materials science as a whole. Due to the network architecture of these materials, imbibement with water often results in uniform swelling and isotropic expansion which scales with the degree of cross-linking. However, the development of internal stresses during swelling can have dramatic consequences, leading to surface instabilities as well as rupture or bursting events. To better understand hydrogel behavior, macroscopic mechanical characterization techniques (e.g. tensile testing, rheometry) are often used, however most commonly these techniques are employed on samples that are in two distinct states: (1) unswollen and without any solvent, or (2) in an equilibrium swelling state where the maximum amount of water has been imbibed. Rarely is the dynamic process of swelling studied, especially in samples where rupture or failure events are observed. To address this gap, here we focus on rupture events in poly(ethylene glycol)-based networks that occur in response to swelling with water. Rupture events were visualized using high-speed imaging, and the influence of swelling on material properties was characterized using dynamic mechanical analysis. We find that rupture events follow a three-stage process that includes a waiting period, a slow fracture period, and a final stage in which a rapid increase in the velocity of crack propagation is observed. We describe this fracture behavior based on changes in material properties that occur during swelling, and highlight how this rupture behavior can be controlled by straight-forward modifications to the hydrogel network structure.

Nonlinear, dissipative phenomena in whole blood clot mechanics

When a thrombus breaks off and embolizes it can occlude vital vessels such as those of the heart, lung, or brain. These thromboembolic conditions are responsible for 1 in 4 deaths worldwide. Thrombus resistance to embolization is driven by its intrinsic fracture toughness as well as other, non-surface-creating dissipative mechanisms. In our current work, we identify and quantify these latter mechanisms toward future studies that aim to delineate fracture from other forms of dissipation. To this end, we use an in vitro thrombus mimic system to produce whole blood clots and explore their dissipative mechanics under simple uniaxial extension, cyclic loading, and stress-relaxation. We found that whole blood clots exhibit Mullins-like effect, hysteresis, permanent set, strain-rate dependence, and nonlinear stress-relaxation. Interestingly, we found that performing these tests under dry or submerged conditions did not change our results. However, performing these tests under room temperature or body temperature conditions yielded differences. Importantly, because we use venous blood our work is most closely related to venous in vivo blood clots. Overall, we have demonstrated that whole blood clots show several dissipative phenomena - similarly to hydrogels - that will be critical to our understanding of thrombus embolization.