Method of image charges for describing deformation of bounded two-dimensional solids with circular inclusions

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

doi:10.1103/physreve.103.053004

Cited by 9 publications

(7 citation statements)

References 57 publications

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“…In §2, this article generalizes prior studies (e.g. [31,39]) of multipolar fields of ellipsoidal inclusions to arbitrary order. Aside from providing an intuitive and computationally cheap means of studying the long and near field of the inclusion, the multipolar expansion of the ellipsoidal inclusion serves as a testing ground for the approach, showcasing how non-obvious known results such as the effect of the inclusion's volume in the far field [40] can be quickly recovered (thereby validating the approach) while facilitating understanding of the near field as well.…”

Section: Introductionmentioning

confidence: 64%

“…In the context of linear elasticity, multipolar field expansions have long been employed to model point defects [24,25], particularly because the trace of the dipolar moment tensor is the relaxation volume of the defect [26], which enables the easy modelling of the dipolar moment tensor if the relaxation volume of the point defect can be calculated from first principles [26,27] or deduced from X-ray diffraction data [28]. Generalized formalisms of the multipolar fields have been offered in the context of reconstruction of seismic sources from estimated low order multipolar moments [29,30], and applied over particular cases to circular voids in plane stress [31], prismatic loops [32], dislocation loops and cracks [33] or to stochastic ensembles of dislocations [34]. They have also been applied to ensembles of dislocations in the context of discrete dislocation dynamics and the fast multipole method [35,36], and in the context of homogenization theory, with the aim of development of effective elastic moduli and constitutive behaviours in composite materials with spherical or ellipsoidal inclusions [37][38][39].…”

Section: Introductionmentioning

confidence: 99%

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The multipolar elastic fields of ellipsoidal and polytopal plastic inclusions

Gurrutxaga-Lerma

2023

Proc. R. Soc. A.

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The article offers a general formulation for the multipolar field expansion of an inclusion. The multipolar moments of arbitrary order for the ellipsoidal inclusion are derived, showing known features of their elastic fields in both the far and near field. Using integer point enumeration theory, the same formulation is extended to all polytopal inclusions, which serve to model faceted inclusions found in, e.g. igneous and metamorphic rocks, particle reinforced composite materials, or as intermetallic precipitates in alloys. A general algorithm for the calculation of the multipolar moments of polytopes of any number of vertices is derived. A number of examples for tetrahedral, cuboidal and dodecahedral inclusions are given. It is shown that the parity of the axial moment function of a polytopal inclusion mirrors the symmetry of the inclusion. This represents the main properties of their elastic fields, including the long- and near-field decay. If the inclusion is symmetric with respect to a given axes, the fields will decay with 1 / r 2 in the far field and 1 / r 4 in the near field. If symmetry along that direction is lost, as is expected in most real inclusions, the decay rate progresses with 1 / r 2 but the near field with 1 / r 3 .

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Section: Introductionmentioning

confidence: 64%

Section: Introductionmentioning

confidence: 99%

The multipolar elastic fields of ellipsoidal and polytopal plastic inclusions

Gurrutxaga-Lerma

2023

Proc. R. Soc. A.

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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 [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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“…where

are the planar position of the i th vehicle and its image charge ( 58 ), R and R v are the radii of the membrane and the vehicle, σ is the area density of the membrane, and

is a membrane constant; the three terms in the solution show, respectively, the contributions of the vehicle height field from the membrane, the weight of the vehicle of interest, and the other vehicles. The last term conceptually acts as an attractive potential (like the Newtonian gravitational potential), whose gradient generates a pairwise attractive force between the vehicles.…”

Section: Development Of a Theory For Reciprocal Field-mediated Intera...mentioning

confidence: 99%

Field-mediated locomotor dynamics on highly deformable surfaces

Ozkan-Aydin

Small

et al. 2022

Proc. Natl. Acad. Sci. U.S.A.

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Studies of active matter—systems consisting of individuals or ensembles of internally driven and damped locomotors—are of interest to physicists studying nonequilibrium dynamics, biologists interested in individuals and swarm locomotion, and engineers designing robot controllers. While principles governing active systems on hard ground or within fluids are well studied, another class of systems exists at deformable interfaces. Such environments can display mixes of fluid-like and elastic features, leading to locomotor dynamics that are strongly influenced by the geometry of the surface, which, in itself, can be a dynamical entity. To gain insight into principles by which locomotors are influenced via a deformation field alone (and can influence other locomotors), we study robot locomotion on an elastic membrane, which we propose as a model of active systems on highly deformable interfaces. As our active agent, we use a differential driven wheeled robotic vehicle which drives straight on flat homogeneous surfaces, but reorients in response to environmental curvature. We monitor the curvature field–mediated dynamics of a single vehicle interacting with a fixed deformation as well as multiple vehicles interacting with each other via local deformations. Single vehicles display precessing orbits in centrally deformed environments, while multiple vehicles influence each other by local deformation fields. The active nature of the system facilitates a differential geometry–inspired mathematical mapping from the vehicle dynamics to those of test particles in a fictitious “spacetime,” allowing further understanding of the dynamics and how to control agent interactions to facilitate or avoid multivehicle membrane-induced cohesion.

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Method of image charges for describing deformation of bounded two-dimensional solids with circular inclusions

Cited by 9 publications

References 57 publications

The multipolar elastic fields of ellipsoidal and polytopal plastic inclusions

The multipolar elastic fields of ellipsoidal and polytopal plastic inclusions

The fluidic memristor: collective phenomena in elastohydrodynamic networks

Field-mediated locomotor dynamics on highly deformable surfaces

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