My research broadly deals with modeling instabilities in a variety of materials ranging from the multi-functional graphene to rubbery materials like PDMS, PMMA etc. Here is the overview of the projects that I am working on.

1. Quantum flexoelectric crinkles in graphene

AFM image of MLG crinkle

Typical curvature distribution of MLG crinkle

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. 

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. 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.

4. 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.

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