Elastic multipole method for describing deformation of infinite two-dimensional solids with circular inclusions

Sarkar, Siddhartha; Čebron, Matjaž; Brojan, Miha; Košmrlj, Andrej

doi:10.1103/physreve.103.053003

Cited by 8 publications

(4 citation statements)

References 68 publications

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“…The numerical value of the coupling constant α depends on material properties and the detailed geometry. It is, in principle, possible to predict the value of α from analytical theories [78][79][80] , or from direct numerical simulations. As shown in the main text, however, the qualitative behavior shown in this work is relatively insensitive to the value of α, we therefore focus on the basic properties of the model and treat α as a fitting parameter.…”

Section: Phenomenological Modelmentioning

confidence: 99%

The fluidic memristor as a collective phenomenon in elastohydrodynamic networks

Martínez-Calvo,

Biviano,

Christensen

et al. 2024

Nat Commun

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Fluid flow networks are ubiquitous and can be found in a broad range of contexts, from human-made systems such as water supply networks to living systems like animal and plant vasculature. In many cases, the elements forming these networks exhibit a highly non-linear pressure-flow relationship. Although we understand how these elements work individually, their collective behavior remains poorly understood. In this work, we combine experiments, theory, and numerical simulations to understand the main mechanisms underlying the collective behavior of soft flow networks with elements that exhibit negative differential resistance. Strikingly, our theoretical analysis and experiments reveal that a minimal network of nonlinear resistors, which we have termed a ‘fluidic memristor’, displays history-dependent resistance. This new class of element can be understood as a collection of hysteresis loops that allows this fluidic system to store information, and it can be directly used as a tunable resistor in fluidic setups. Our results provide insights that can inform other applications of fluid flow networks in soft materials science, biomedical settings, and soft robotics, and may also motivate new understanding of the flow networks involved in animal and plant physiology.

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Section: Phenomenological Modelmentioning

confidence: 99%

The fluidic memristor as a collective phenomenon in elastohydrodynamic networks

Martínez-Calvo,

Biviano,

Christensen

et al. 2024

Nat Commun

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show abstract

“…The numerical value of the coupling constant α depends on material properties and the detailed geometry. It is, in principle, possible to predict the value of α from analytical theories [63][64][65], or from direct numerical simulations. As shown in the main text, however, the qualitative behavior shown in this work is relatively insensitive to the value of α, we therefore focus on the basic properties of the model and treat α as a fitting parameter.…”

Section: Phenomenological Modelmentioning

confidence: 99%

The fluidic memristor: collective phenomena in elastohydrodynamic networks

Martínez-Calvo¹,

Biviano²,

Christensen³

et al. 2023

Preprint

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Fluid flow networks are ubiquitous and can be found in a broad range of contexts, from human-made systems such as water supply networks to living systems like animal and plant vasculature. In many cases, the elements forming these networks exhibit a highly non-linear pressure-flow relationship. Although we understand how these elements work individually, their collective behavior remains poorly understood. In this work, we combine experiments, theory, and numerical simulations to understand the main mechanisms underlying the collective behavior of soft flow networks with elements that exhibit negative differential resistance. Strikingly, our theoretical analysis and experiments reveal that a minimal network of nonlinear resistors, which we have termed a 'fluidic memristor', displays history-dependent resistance. This new class of element can be understood as a collection of hysteresis loops that allows this fluidic system to store information. Our work provides insights that may inform new applications of fluid flow networks in soft materials science, biomedical settings, and soft robotics, and may also motivate new understanding of the flow networks involved in animal and plant physiology.

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“…An extensive presentation and discussion of elastic charges within the linear theory is given in Ref. [18][19][20]. A generalization to nonlinear elasticity can be found in Ref.…”

Section: B Background: Elastic Chargesmentioning

confidence: 99%

Anomalous Elasticity and Screening in Amorphous Solids

Lemaître,

Mondal,

Moshe

et al. 2021

Preprint

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Amorphous solids appear to react elastically to small external strains, but in contrast to ideal elastic media, plastic responses abound immediately, at any value of the strain. Such plastic responses are quasi-localized in nature, with the "cheapest" one being a quadrupolar source. The existence of such plastic responses results in screened elasticity in which strains and stresses can either quantitatively or qualitatively differ from the un-screened theory, depending on the specific screening mechanism. Here we offer a theory of such screening effects by plastic quadrupoles, dipoles and monopoles, explain their natural appearance, and point out the analogy to electrostatic screening by electric charges and dipoles. For low density of quadrupoles the effect is to normalize the elastic moduli without a qualitative change compared to pure elasticity theory; for higher density of quadrupoles the screening effects result in qualitative changes. Predictions for the spatial dependence of displacement fields caused by local sources of strains are provided and compared to numerical simulations. We find that anomalous elasticity is richer than electrostatics in having a screening mode that does not appear in the electrostatic analog.

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Elastic multipole method for describing deformation of infinite two-dimensional solids with circular inclusions

Cited by 8 publications

References 68 publications

The fluidic memristor as a collective phenomenon in elastohydrodynamic networks

The fluidic memristor as a collective phenomenon in elastohydrodynamic networks

The fluidic memristor: collective phenomena in elastohydrodynamic networks

Anomalous Elasticity and Screening in Amorphous Solids

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