Continuum mechanics of a cellular tissue model

Kupferman, Raz; Maman, Ben; Moshe, Michael

doi:10.1016/j.jmps.2020.104085

Cited by 12 publications

(7 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It was shown in [13] that this energy functional yields the rigidity transition and captures the response of the VM to uniaxial deformations. Recent work has additionally proved [37] that a rigorous coarse-graining of the discrete triangular VM converges yields the continuum model proposed in [13].…”

Section: Summary and Discussionmentioning

confidence: 98%

“…In the compatible regime the ground state is degenerate, as shown in FIG. 1(a), where the flat region corresponds to a continuous set of rest configurations [13,37]. This means that when subject, for instance, to a small uniaxial or shear deformation, the system can accommodate the deformation by finding a new zero energy configuration corresponding to the deformed shape, resulting in vanishing elastic constant 𝐺.…”

Section: Linear Mechanical Responsementioning

confidence: 99%

See 1 more Smart Citation

Anomalous elasticity of cellular tissue vertex model

Hernandez,

Staddon,

Bowick

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

Vertex Models, as used to describe cellular tissue, have an energy controlled by deviations from both a target area and a target perimeter. The constrained nonlinear relation between area and perimeter, as well as subtleties in selecting the appropriate reference state, lead to a host of interesting mechanical responses. Here we provide a mean-field treatment of a highly simplified model: a network of regular polygons with no topological rearrangements. Since all polygons deform in the same way we need only analyze the ground states and the response to deformations of a single polygon (cell). The model exhibits the known transition between a fluid/compatible state, where the cell can accommodate both target area and perimeter, and a rigid/incompatible state. The fluid state has a manifold of degenerate zero energy states. The rigid state has a single gapped ground state. We show that linear elasticity fails to describe the response of the vertex model to even infinitesimal deformations in both regimes and that the response depends on the precise deformation protocol. We give a pictorial representation in configuration space that reveals that the complex elastic response of the Vertex Model arises from the presence of two distinct sets of reference configurations (associated with target area and target perimeter) that may be either compatible or incompatible, as well as from the underconstrained nature of the model energy. An important result of our work is that the elasticity of the Vertex Model cannot be captured by a Taylor expansion of the energy for small strains, as Hessian and higher order gradients are ill-defined.

show abstract

Section: Summary and Discussionmentioning

confidence: 98%

Section: Linear Mechanical Responsementioning

confidence: 99%

Anomalous elasticity of cellular tissue vertex model

Hernandez,

Staddon,

Bowick

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…1 and taking the idea of "cells as shapes" seriously, representing the confluent tissue by polygonal or polyhedral tilings of space [26][27][28][29][30][31][32][33]. These fundamentally geometrical models of cells have fascinating properties -in some cases they display the sort of behavior one might expect given roughly any reasonably-biologically-informed agent-based model in which each cell corresponds to just one or a handful of degrees of freedom, but in other cases they can be shown to support exotic mechanical states [32,34,35] and display unusual structural or dynamical scaling [36,37]. To investigate these unusual properties, in recent years there have been substantial advances in the efficient numerical simulations of these and related agent-based models of dense tissue [25,[38][39][40][41].…”

Section: Geometric Models Of Dense Tissuementioning

confidence: 99%

Non-metric interaction rules in models of active matter

Sussman

2021

Preprint

View full text Add to dashboard Cite

This article is based on lecture notes for the Marie Curie Training school "Initial Training on Numerical Methods for Active Matter." It is common in the study of a dizzying array of soft matter systems to perform agent-based simulations of particles interacting via conservative and often shortranged forces. In this context, well-established algorithms for efficiently computing the set of pairs of interacting particles have established excellent open-source packages to efficiently simulate large systems over long time scales -a crucial consideration given the separation in time-and length-scales often observed in soft matter. What happens, though, when we think more broadly about what it means to construct a neighbor list? What if interactions are non-reciprocal, or if the "range" of an interaction is determined not by a distance scale but according to some other consideration? As the field of soft and active matter increasingly considers the properties of living matter -from the cellular to the super-organismal scale -these questions become increasingly relevant, and encourage us to think about new physical and computational paradigms in the modeling of active matter. In this chapter we examine case studies in the use of non-metric interactions.

show abstract

“…When p 0 ≥ p Ã 0 , the unstrained tissue is fluid and G 0 ¼ 0. This solid-fluid transition at γ ¼ 0 is now well understood in terms of a Maxwell constraint-counting approach [71,78] and as driven by geometric incompatibility [71,74,[79][80][81].…”

mentioning

confidence: 98%