Hydraulic fracture geometry in ultrasoft polymer networks

Yang, Steven J.; Bahk, Davin; Kim, Jiho; Kataruka, Amrita; Dunn, Alison C.; Hutchens, Shelby B.

doi:10.1007/s10704-019-00380-y

Cited by 17 publications

(10 citation statements)

References 31 publications

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“…In contrast, internal pressurization of a defect, by injection of an incompressible fluid [33,34,35], by phase separation [36,37], or by the growth of an embedded inclusion [38,39], can allow for complete control over the expansion process, and is a promising avenue for measuring material properties and understanding the initiation of damage and fracture [40,41,42,43,44]. In these settings however, the defect can have intricate shapes [27,45,46] and it is not obvious how the deformation field generated via internal pressurization translates to explain failure of the bulk material, as induced by application of external loads.…”

Section: The Theorem and Its Applicationsmentioning

confidence: 99%

A Reciprocal Theorem for Finite Deformations in Incompressible Bodies

Henzel¹,

Senthilnathan²,

Cohen³

2022

Preprint

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The reciprocal theorems of Maxwell and Betti are foundational in mechanics but have so far been restricted to infinitesimal deformations in elastic bodies. In this manuscript, we present a reciprocal theorem that relates solutions of a specific class of large deformation boundary value problems for incompressible bodies; these solutions are shown to identically satisfy the Maxwell-Betti theorem. The theorem has several potential applications such as development of alternative convenient experimental setups for the study of material failure through bulk and interfacial cavitation, and leveraging easier numerical implementation of equivalent auxiliary boundary value problems. The following salient features of the theorem are noted: (i) it applies to dynamics in addition to statics, (ii) it allows for large deformations, (iii) generic body shapes with several potential holes, and (iv) any general type of boundary conditions.

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Section: The Theorem and Its Applicationsmentioning

confidence: 99%

A Reciprocal Theorem for Finite Deformations in Incompressible Bodies

Henzel¹,

Senthilnathan²,

Cohen³

2022

Preprint

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“…These elastomers are also common in fundamental research on soft matter physics and mechanics. For example, studies on soft adhesion, wetting, cavitation, and cell–surface interactions frequently implement PDMS as a model material. PDMS is used because it is commercially available (e.g., Sylgard 184), easy to prepare, and easy to tune the elastic modulus from a few megapascal down to a few kilopascal .…”

Section: Introductionmentioning

confidence: 99%

“…PDMS is used because it is commercially available (e.g., Sylgard 184), easy to prepare, and easy to tune the elastic modulus from a few megapascal down to a few kilopascal . This simple modulus control has enabled the growing and vast use of commercial PDMS elastomers with moduli below 100 kPa . In order to decrease the modulus, the amount of crosslinking agent is reduced relative to the reactive silicone base in many commercial elastomers, which come as two‐part kits.…”

Section: Introductionmentioning

confidence: 99%

Extracting uncrosslinked material from low modulus sylgard 184 and the effect on mechanical properties

Glover

McLaughlin

McFarland

et al. 2020

Journal of Polymer Science

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Commercial silicone elastomers are commonly used in soft materials research due to their easily tunable mechanical properties.However, conventional polydimethylsiloxane (PDMS) elastomers with moduli below $100 kPa contain uncrosslinked free molecules, which play a significant role in their behavior. To utilize these materials, it is important to quantify what role these free molecules play in the mechanical response before and after their removal. We present a simple and inexpensive extraction method that enables the removal of free molecules from a lightly crosslinked sheet of Sylgard 184, a commercially available PDMS elastomer. The materials can contain a majority of free molecules yet maintain a thin and flat geometry without fractures after extraction. Subsequently, we compare the modulus, maximum stretchability, and hysteresis behavior with mixing ratios ranging from 60:1 to 30:1, before and after extraction. We show that the modulus, maximum stretchability, and dissipation increase upon extraction. Moreover, our approach offers a route to prepare crosslinked silicone elastomers with a modulus as low as $20 kPa without free molecules from a commercially available kit.

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“…The organization and dynamics of the separating phases, as they condense and grow, is strongly influenced by the elastic resistance of the matrix. Finally, emerging techniques for characterization of soft materials grow fluid filled cavities inside the material to estimate its nonlinear properties (Kundu and Crosby, 2009;Raayai-Ardakani et al, 2019;Yang et al, 2019;Chockalingam et al, 2021). Notably, these experiments also indicate morphological transitions from regular-shaped cavities to branched fracture patterns as the cavity grows (Raayai-Ardakani et al, 2019;Yang et al, 2019;Morelle et al, 2021).…”

Section: Introductionmentioning

confidence: 96%

Nonlinear Inclusion Theory with Application to the Growth and Morphogenesis of a Confined Body

Li,

Kothari,

Senthilnathan

et al. 2021

Preprint

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One of the most celebrated contributions to the study of the mechanical behavior of materials is due to J.D. Eshelby, who in the late 50s revolutionized our understanding of the elastic stress and strain fields due to an ellipsoidal inclusion/inhomogeneity that undergoes a transformation of shape and size. While Eshelby's work laid the foundation for significant advancements in various fields, including fracture mechanics, theory of phase transitions, and homogenization methods, its extension into the range of large deformations, and to situations in which the material can actively reorganize in response to the finite transformation strain, is in a nascent state. Beyond the theoretical difficulties imposed by highly nonlinear material response, a major hindrance has been the absence of experimental observations that can elucidate the intricacies that arise in this regime. To address this limitation, our experimental observations reveal the key morphogenesis steps of Vibrio cholerae biofilms embedded in hydrogels, as they grow by four orders of magnitude from their initial size. Using the biofilm growth as a case study, our theoretical model considers various growth scenarios and employs two different and complimentary methods to obtain equilibrium solutions. A particular emphasis is put on determining the natural growth path of an inclusion that optimizes its shape in response to the confinement, and the onset of damage in the matrix, which together explain the observed behavior of biofilms. Beyond bacterial biofilms, this work sheds light on the role of mechanics in determining the morphogenesis pathways of confined growing bodies and thus applies to a broad range of phenomena that are ubiquitous in both natural and engineered material systems.

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Hydraulic fracture geometry in ultrasoft polymer networks

Cited by 17 publications

References 31 publications

A Reciprocal Theorem for Finite Deformations in Incompressible Bodies

A Reciprocal Theorem for Finite Deformations in Incompressible Bodies

Extracting uncrosslinked material from low modulus sylgard 184 and the effect on mechanical properties

Nonlinear Inclusion Theory with Application to the Growth and Morphogenesis of a Confined Body

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