My research broadly deals with modeling instabilities, across lengthscales and in a variety of materials ranging from the multi-functional graphene to rubbery materials like PDMS, PMMA etc. Here is the overview of my research.
1. Quantum flexoelectric crinkles in graphene
Graphene develops electrical polarization when it is bent. This property of graphene is called as 'quantum flexoelectricity' since it arises due to distortion of electron cloud upon bending. Flexoelectricity has profound implications in the buckling response of graphene, especially multilayer graphene (MLG). MLG when gently compressed, instead of buckling into a sinusoidal shape, buckles into kink-shaped crinkles. The dipole-dipole interactions, both intralayer and interlayer, provide the energy reduction through a localized and oscillatory curvature distribution.
AFM image of MLG crinkle
Typical curvature distribution in an MLG crinkle
A very subtle but critical finding is that flexoelectricity in graphene switches the bifurcation from typically supercritical to subcritical. If the flexoelectricity effect is turned off, a much smoother curvature distribution is observed. The boundary layer of the localized curvature is approximately 2 nm wide. The dipole magnitude is directly proportional to the curvature. Such a narrow boundary layer focuses the flexoelectric charges into nearly a line charge along the crinkle ridge/valley which is controllable by external strain. This opens up exciting possibilities including manipulating charged and polarizable molecules through crinkles.
This is a brief overview - for more exciting findings and details take a look at our paper.
2. Dielectricity-Flexoelectricity coupling in graphene
We recently discovered that graphene, especially multilayer graphene, upon buckling forms kink-shaped elastic crinkles. We examine the coupling of flexoelectricity and dielectricity in multilayer graphene (MLG) in detail. A thermodynamically motivated, non-local constitutive law for modeling the coupling is proposed. The flexoelectric-dielectric coupling is critical for the existence of crinkle buckling mode and a uniform bending model cannot be directly applied to a general non-uniform case. The non-local model can be simplified in adequate situations to a lumped model - either uniform curvature or e-local model (discussed in 1). In addition to this, the mathematical details of the thermodynamic formalism and its further reduction under different scenarios are treated.
Buckyball adsorption on HOPG
Positively (P-type)/ Negatively (N-type) charged crinkles
The non-local formalism allows an accurate prediction of the induced flexoelectric charges on graphene crinkles. These charges can be either positive or negative depending on the curvature. We demonstrate the existence of these charges experimentally by adsorption study of buckyballs on HOPG. The inter-buckyball spacing predicted by the model is in agreement with experiments, indicating that flexoelectricity of graphene is the mechanism behind the aligned adsorption. Check out the paper for more.
3. Elastic effects in liquid-liquid phase separation
Physical systems consisting of an elastic matrix permeated by ﬂuid mixture are ubiquitous, with examples ranging from morphogenesis of a single biological cell to the migration of greenhouse gases in sediments. Recent experimental studies show that the presence of the elastic networks in these systems signiﬁcantly alters their phase-separation response by imposing an energetic cost to the growth of droplets. However, a quantitative understanding of the role played by elasticity is lacking. Our paper bridges this gap by building a comprehensive theoretical framework to analyze the effect of elasticity on the phase separation of a binary mixture in soft, nonlinear solids.
We employ an energy-based approach that captures both the short-time quasi-equilibrium and the long-time evolution of the phase separation, in elastically homogeneous as well as heterogeneous materials, to determine the constitutive sensitivities. At the short timescale, we find that elasticity arrests phase separation and leads to droplets of characteristic size (determined by the stiffness).
Short Timescale : elasticity arrests phase separation leading to mono-disperse droplets
At the longer timescale, our theory predicts a droplet dissolution front in heterogeneous materials. Crucially, we also ﬁnd a nonlinear effect of elasticity on the dynamics, which challenges the current understanding in the literature. We quantify the thermodynamic driving forces to identify diffusion-limited and dissolution-limited regimes of front propagation. Our ﬁndings are applicable to a variety of material systems including food, metals, and aquatic sediments, and further substantiate the hypothesis that biological systems exploit such mechanisms to regulate their function.
Long Timescale : elastic heterogeneity can lead to droplet-dissolution front
4. Peeling of soft adhesive layers
We study a representative setting — peeling of an adhesive layer by pushing on it — that underlies many complex processes ranging from Schallamach waves to evolution of geological formations to movement of cells.In a controlled-displacement setting, the layer partially detaches via a subcritical instability and the motion continues until arrested, by jamming of the two lobes. Using numerical solutions and scaling analysis, we quantitatively describe the equilibrium shapes and obtain constitutive sensitivities of jamming process to material and interface properties. We conclude with a way to delay or avoid jamming altogether by tunable interface properties. More details here.
Controlled peeling of a soft, adhesive layer that eventually leads to jamming
5. Thermo-mechanically coupled finite strain model for phase-transitioning steels at cryogenic temperature
Austenitic steels are widely used for cryogenic temperature applications, for instance in LNG transportation pipes. Metastable austenitic steels show significant changes in constitutive response due to plastic-strain driven phase transition to martensite and this transition is accelerated at cryogenic temperatures. This leads to a second strain hardening which is critical to model the accurate response of complex structures (like corrugated pipes). We developed a model and the simulation capability to account for the phase transitions and complex thermo-mechanical history for austenitic steels and validated it against full-scale C-pipe experiments conducted at cryogenic temperatures. Take a look at the paper for details.
6. Creasing in soft materials
Soft materials are susceptible to a variety of instabilities that lead to an array of surface patterns including wrinkles, folds and creases. Crease is a cusp shaped surface pattern and one situation where creasing is observed is on the surface of a homogenous half-space, of say neo-hookean material, under lateral compression. The critical compressive strain for this case is found by many to be 35.6 %. We are focused on analytically modeling the crease to pinpoint this critical compressive strain.