arXiv subjects

Ayan Roychowdhury

Publications and source records attributed to Ayan Roychowdhury.

9 recordsLinked to original sources

arXiv2025

Active drive towards elastic spinodals

Active matter, exemplified by adaptive living materials such as the actomyosin cytoskeleton, can navigate material parameter space dynamically, leading to unconventional mechanical responses. In particular, it can self-drive toward elastic spinodal regimes, where inhomogeneous floppy modes induce elastic degeneracy and enable a controlled interplay between rigidity loss and recovery. Proximity to such marginal states leads to stress localization and the formation of force chains that can be actively assembled and disassembled. Here, we extend the classical notion of spinodal states to active solids and demonstrate how these extreme mechanical regimes can be actively accessed. Moreover, we show that in a nonlinear setting, crossing elastic spinodals generates new energy wells and makes force channeling an intrinsic feature of the emerging microstructure.

cond-mat.soft↗

arXiv2025

Emergence of Tension Chains and Active Force Patterning

Viewed under a fluorescence microscope, the actomyosin cytoskeleton presents vivid streaks of lines together with persistent oscillatory waves. Using an active hydrodynamic approach, we show how a uniform distribution of single or mixture of contractile stresslets spontaneously segregate, followed by the formation of singular structures of high contractility (tension chains) in finite time. Simultaneously, the collection of stresslets exhibit travelling waves and swapping as a consequence of nonreciprocity. In the finite geometry of the cell, the collection of active tension chains can form an active web held together by specific anchoring at the cell boundary. On the other hand, preferential wetting at the cell boundary can reinforce active segregation in a mixture of stresslets leading to stratification.

cond-mat.soft↗

arXiv2025

Segregation, Finite Time Elastic Singularities and Coarsening in Renewable Active Matter

Material renewability in active living systems, such as in cells and tissues, can drive the large-scale patterning of forces, with distinctive phenotypic consequences. This is especially significant in the cell cytoskeleton, where multiple species of myosin bound to actin, apply differential contractile stresses and undergo differential turnover, giving rise to patterned force channeling. Here we study the dynamical patterning of stresses that emerge in a hydrodynamic description of a renewable active actomyosin elastomer comprising two myosin species. Our analytical framework also holds for an actomyosin elastomer with a single myosin species. We find that a uniform active contractile elastomer spontaneously segregates into spinodal stress patterns, followed by a finite-time collapse into tension carrying singular structures that display self-similar scaling and caustics. Our numerical analysis carried out in 1D, shows that these singular structures move and merge, and gradually result in a slow coarsening dynamics. We discuss the implications of our findings to the emergence of stress fibers and the spatial patterning of actomyosin. Our study suggests, that with state-dependent turnover of crosslinkers and myosin, the in vivo cytoskeleton can navigate through the space of material parameters to achieve a variety of functional phenotypes.

cond-mat.soft↗

arXiv2022

Defects and Metric Anomalies in Föppl-von Kármán Surfaces

A general framework is developed to study the deformation and stress response in F{ö}ppl-von K{á}rm{á}n shallow shells for a given distribution of defects, such as dislocations, disclinations, and interstitials, and metric anomalies, such as thermal and growth strains. The theory includes dislocations and disclinations whose defect lines can both pierce the two-dimensional surface and lie within the surface. An essential aspect of the theory is the derivation of strain incompatibility relations for stretching and bending strains with incompatibility sources in terms of various defect and metric anomaly densities. The incompatibility relations are combined with balance laws and constitutive assumptions to obtain the inhomogeneous F{ö}ppl-von K{á}rm{á}n equations for shallow shells. Several boundary value problems are posed, and solved numerically, by first considering only dislocations and then disclinations coupled with growth strains.

cond-mat.soft↗

arXiv2017

Dislocations, disclinations, and metric anomalies as sources of global strain incompatibility in thin shells

The strain incompatibility equations are discussed for nonlinear Kirchhoff-Love shells with sources of inhomogeneity arising due to a distribution of topological defects, such as dislocations and disclinations, and metric anomalies, such as point defects, thermal strains, and biological growth. The incompatibility equations are given for all topological surfaces, with or without boundary, which are isometrically embeddable in a 3-dimensional Euclidean space.

cond-mat.soft↗

arXiv2017

On structured surfaces with defects: geometry, strain incompatibility, internal stress, and natural shapes

Given a distribution of defects on a structured surface, such as those represented by 2-dimensional crystalline materials, liquid crystalline surfaces, and thin sandwiched shells, what is the resulting stress field and the deformed shape? Motivated by this concern, we first classify, and quantify, the translational, rotational, and metrical defects allowable over a broad class of structured surfaces. With an appropriate notion of strain, the defect densities are then shown to appear as sources of strain incompatibility. The strain incompatibility relations, with appropriate kinematical assumptions on the decomposition of strain into elastic and plastic parts, and the stress equilibrium relations, with a suitable choice of material response, provide the necessary equations for determining both the internal stress field and the deformed shape. We demonstrate this by applying our theory to Kirchhoff-Love shells with a kinematics which allows for small in-surface strains but moderately large rotations.

cond-mat.mtrl-sci↗

arXiv2016

Non-metric connection and metric anomalies in materially uniform elastic solids

Metric anomalies arising from a distribution of point defects (intrinsic interstitials, vacancies, point stacking faults), thermal deformation, biological growth, etc. are well known sources of material inhomogeneity and internal stress. By emphasizing the geometric nature of such anomalies we seek their representations for materially uniform crystalline elastic solids. In particular, we introduce a quasi-plastic deformation framework where the multiplicative decomposition of the total deformation gradient into an elastic and a plastic deformation is established such that the plastic deformation is further decomposed multiplicatively in terms of a deformation due to dislocations and another due to metric anomalies. We discuss our work in the context of quasi-plastic strain formulation and Weyl geometry. We also derive a general form of metric anomalies which yield a zero stress field in the absence of other inhomogeneities and any external sources of stress.

cond-mat.mtrl-sci↗

arXiv2015

Material homogeneity and strain compatibility in thin elastic shells

We discuss several issues regarding material homogeneity and strain compatibility for materially uniform thin elastic shells from the viewpoint of a 3-dimensional theory, with small thickness, as well as a 2-dimensional Cosserat theory. A relationship between inhomogeneity and incompatibility measures under the two descriptions is developed. More specifically, we obtain explicit forms of intrinsic dislocation density tensors characterising inhomogeneity of a dislocated Cosserat shell. We also formulate a system of governing equations for the residual stress field emerging out of strain incompatibilities which in turn are related to inhomogeneities. The equations are simplified for several cases under the Kirchhoff-Love assumption.

math-ph↗

arXiv2013

Geometry of Defects in Solids

The appealing connection between non-Euclidean geometries and defects in solids is brought forth in this article. Drawing a correspondence between the nature of a defect and a specific geometric property of the material space not only illuminates the underlying structure of defects in solids but also provides an unambiguous way to represent defect densities within a physical theory. We present a rigorous background of the relevant concepts from classical differential geometry, as well as illustrations of isolated defects in a lattice, to motivate the relationship between continuous defect densities and various tensor fields in differential geometry. We identify the Riemann-Christoffel tensor (or curvature tensor), the Cartan tensor (or torsion tensor), and the nonmetricity tensor (obtained from the covariant derivative of the metric tensor), associated with the material space, with the density of disclinations, dislocations, and point-defects (vacancies, interstitials, substitutional), respectively. We end our discussion with remarks on the elastic stress field associated with defect distribution and on the analogy between the present theory and the general theory of relativity.

cond-mat.mtrl-sci↗