Probing local nonlinear viscoelastic properties in soft materials

Chockalingam, Sreekumar; Roth, Christian C.; Henzel, Thomas; Cohen, Tal

doi:10.1016/j.jmps.2020.104172

Cited by 24 publications

(20 citation statements)

References 57 publications

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“…However, the mechanical instability induced by application of external loads beyond a critical threshold is an extremely fast and uncontrollable process; attempts to experimentally study these internal ruptures are thus challenging [31,32]. 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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“…where the pressure arising from the elastic material resistance, P m , is defined in (A 9). Alternative derivations of the above equation of motion can be found in [42,43,51].…”

Section: (B) Equation Of Motion Of Cavitymentioning

confidence: 99%

“…Accounting for the compressibility of the confining medium will lead to loss of energy through acoustic waves and thus damping of the cavity motion [15,32,34], which we neglect in our modelling here. A detailed derivation of the governing equations can be found in several earlier studies [42,43,51] and is provided for a general constitutive model in appendix A, for completeness. We consider a spherical cavity embedded in the confining solid, subjected to internal pressure p and an externally applied remote tension pext.…”

Section: Theorymentioning

confidence: 99%

Thermo-chemo-mechanically coupled cavity dynamics and the emergence of multi-phase bursts

2022

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Understanding the dynamics induced by confined thermo-chemical processes occurring inside a solid medium is a fundamental problem of interest in several applications, such as hotspot formation and micro-explosions in energetic materials and laser-induced cavitation for energy focusing and material characterization. In recent years, advanced experimental capabilities have uncovered elusive behaviours in such systems, including temperature spikes that emerge at short timescales, and multi-phase explosions. By coupling the mechanics of the solid, the thermodynamics, and the chemical kinetics of the decomposition reactions, the theoretical model developed here explains and demonstrates these phenomena. The dimensionless response of the system is studied numerically and analytical expressions for the mechanical response limits are derived. These results should be useful in guiding future experiments and in explaining phenomena that may emerge at various length and timescales.

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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: 95%

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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Probing local nonlinear viscoelastic properties in soft materials

Cited by 24 publications

References 57 publications

A Reciprocal Theorem for Finite Deformations in Incompressible Bodies

A Reciprocal Theorem for Finite Deformations in Incompressible Bodies

Thermo-chemo-mechanically coupled cavity dynamics and the emergence of multi-phase bursts

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

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