arXiv subjects

Vishnu V. Krishnan

Publications and source records attributed to Vishnu V. Krishnan.

5 recordsLinked to original sources

arXiv2025

Yielding in amorphous solids reveals an age-dependent intrinsic lengthscale

Understanding how amorphous solids yield under shear is central to predicting material failure, yet prescribing reliable local yielding criteria remains a fundamental challenge. Here, through a mesoscale analysis of localized yielding, we reveal an intrinsic length scale (ζ) that governs local failure, and demonstrate that ζgrows with the age of the system. The age dependence shows up not only in the features of the distribution of local yield stress but also in the pseudogap exponent θ, which provides a measure of marginal stability of the amorphous solids. These insights are made possible by a new method, termed the soft matrix approach, that allows local regions of an amorphous solid to yield within a minimally constrained, elastically coupled environment. By overcoming key limitations of earlier techniques, our approach provides a robust platform for probing failure mechanisms, particularly in soft disordered materials and paves the way for improved elastoplastic modeling of disordered solids.

cond-mat.soft↗

arXiv2023

Enhanced Vibrational Stability in Glass Droplets

We show through simulations of amorphous solids prepared in open boundary conditions that they possess significantly fewer low-frequency vibrational modes compared to their periodic boundary counterparts. Specifically, using measurements of the vibrational density of states, we find that the $D(ω) \sim ω^4$ law changes to $D(ω) \sim ω^δ$ with $δ\approx 5$ in two dimensions and $δ\approx 4.5$ in three dimensions. Crucially, this enhanced stability is achieved when utilizing slow annealing protocols to generate solid configurations. We perform an anharmonic analysis of the minima corresponding to the lowest-frequency modes in such open-boundary systems and discuss their correlation with the density of states. A study of various system sizes further reveals that small systems display a higher degree of localization in vibrations. Lastly, we confine open-boundary solids in order to introduce macroscopic stresses in the system which are absent in the unconfined system, and find that the $D(ω) \sim ω^4$ behavior is recovered.

cond-mat.soft↗

arXiv2021

Annealing effects of multidirectional oscillatory shear in model glass formers

We study the effects of cyclic, athermal quasi-static shear on a model glass-forming system in three dimensions. We utilize the three available orthogonal shear planes, namely $XY, YZ \text{ and } XZ$ to better explore the energy landscape. Using measurements of the stroboscopic $(γ= 0)$ energy, we study the effects of using an orthogonal shear direction to perturb unidirectional steady-states. We find that that each sequence of the unidirectional protocol leads to compaction with the universal, $ΔE \sim N^{-1}$ behavior as a function of the number of cycles, $N$. Additionally we find that cyclic shear utilizing multiple shear planes presents hierarchical compaction, producing progressively lower steady state energies compared to a protocol involving unidirectional cyclic shear alone. Furthermore, with the periodicity of the stroboscopic energy as reference, we show that it is possible to achieve steady state limit-cycles of tunable periodicities using different combinations of the three orthogonal strain directions. We find that such protocols exhibit better annealing as compared to protocols with steady states created using unidirectional shear. Importantly, we find a non-trivial trend in the annealing energy and the period of the steady-state limit-cycle, with an aperiodic protocol appearing to produce the most well annealed states. Finally, we compare the phase diagram of the average steady state energy $\langle E_{\text{S.S.}} \rangle$, as a function of the shearing amplitude $γ_{\max}$, using unidirectional and multidirectional protocols, and find that the universal features are preserved.

cond-mat.dis-nn↗

arXiv2021

Universal non-Debye low-frequency vibrations in sheared amorphous solids

We study energy minimized configurations of amorphous solids with a simple shear degree of freedom. We show that the low-frequency regime of the vibrational density of states of structural glass formers is crucially sensitive to the stress-ensemble from which the configurations are sampled. In both two and three dimensions, a shear-stabilized ensemble displays a $D(ω_{\min}) \sim ω^{5}_{\min}$ regime, as opposed to the $ω^{4}_{\min}$ regime observed under unstrained conditions. We also study an ensemble of two dimensional, strained amorphous solids near a plastic event. We show that the minimum eigenvalue distribution at a strain $γ$ near the plastic event occurring at $γ_{P}$, displays a collapse when scaled by $\sqrt{γ_P - γ}$, and with the number of particles as $N^{-0.22}$. Notably, at low-frequencies, this scaled distribution displays a robust $D(ω_{\min}) \sim ω^{6}_{\min}$ power-law regime, which survives in the large $N$ limit. Finally, we probe the universal properties of this ensemble through a characterization of the second and third eigenvalues of the Hessian matrix near a plastic event.

cond-mat.dis-nn↗

arXiv2020

Singularities in Hessian element distributions of amorphous media

We show that the distribution of elements $H$ in the Hessian matrices associated with amorphous materials exhibit singularities $P(H) \sim {\lvert H \rvert}^γ$ with an exponent $γ< 0$, as $\lvert H \rvert \to 0$. We exploit the rotational invariance of the underlying disorder in amorphous structures to derive these exponents exactly for systems interacting via radially symmetric potentials. We show that $γ$ depends only on the degree of smoothness $n$ of the potential of interaction between the constituent particles at the cut-off distance, independent of the details of interaction in both two and three dimensions. We verify our predictions with numerical simulations of models of structural glass formers. Finally, we show that such singularities affect the stability of amorphous solids, through the distributions of the minimum eigenvalue of the Hessian matrix.

cond-mat.dis-nn↗