## Selected projects from my academic research as a physicist and material scientist

### Fracture in Fractal, Hierarchical, Metamaterials

A ladder of length scales

Recent advances in large area high resolution additive manufacturing have enabled researchers to produces macroscopic samples of materials with several orders of hierarchical length scales and sub-structure. These materials may find advanced structural applications. Thus, it is of utmost importance to develop an understanding of their mechanical properties. Toughness and damage tolerance are two of the most important properties of a structural materials. Yet, our theoretical understanding of toughness and damage tolerance of hierarchical materials is very limited. In this work we develop a theory for the toughness and damage tolerance of these fascinating materials. *A pre-print can be found at https://arxiv.org/abs/1611.01719*

### High Entropy Alloys (HEAs)

Twinning and strain-hardening

HEAs are a new class of alloys that are equi-atomic mixtures of five or more elements; the five component CoCrFeMnNi alloy (Cantor’s alloy) being an example. Contrast this with steel, which is primarily composed of just one element (iron). Some HEAs have been demonstrated to have superior combination of strength and ductility, which is a direct result of continuous strain hardening observed in these alloys. I am engaged in a theoretical and experimental study to understand the effect of twinning on strain hardening in Cantor’s alloy.

### Quazibrittle Fracture In Concrete

A disordered cohesive zone approach

Concrete is a quasibrittle material – it is not ductile in the same sense as metals are, yet it can accumulate significant damage before ultimate failure. Derek Fung (undergraduate student) and I are studying fracture in concrete by using disordered cohesive zone modeling in ABAQUS. The goal is to understand the length scale and disorder dependence of strength of concrete – the so called ‘structural size effect’. This study combines tools from statistical mechanics with FEM and cohesive zone modeling. Some preliminary notes are available on request.

### Grain Boundary Energy in 2D Materials

*(Published, RCS Advances)*

Frank-Bilby, Read-Shockley Type Modeling

Grain boundary energy is a fundamental property that has a profound effect on material processes such as grain growth. I have collaborated with Dr. Colin Ophus and Prof. Robert O. Ritchie at LBL to develop a continuum theory of GB energy in Graphene. The figure shows a fit of the theory to the simulation data. We have simulated the energies of about 79,000 grain boundaries to construct this figure. *This work was published in RCS Advances. A PDF is available here. A pre-print can be found at http://arxiv.org/abs/1611.06592. Some relevant code can be found at this Github repo.*

### Toughness in 2D Materials *(Published, Nature Communications)*

A Statistical Theory

The class of 2D materials has rapidly expanded from just graphene to now include silicene, stanene, TMDCs, thin oxides etc. Many of these materials are brittle, and thus it is necessary to develop an understanding of the statistical distribution of their strength and toughness. I, with Prof. Robert Ritchie, have developed a statistical theory of the grain size dependence of toughness in graphene. This work was published in* Nature Communications. A pre-print can be found at http://arxiv.org/abs/1602.00030*

### Annealing Polycrystalline Graphene *(Published, PRB)*

A Centeroidal Voronoi Tessellation Approach

Experimentally observed polycrystalline graphene is almost always composed of carbon atoms arranged in hexagons, or pentagon-heptagon pairs. However, generating a similar morphology in simulation has been challenging. I have collaborated with LBL scientists Dr. Colin Ophus, Dr. Haider Rasool, and Prof. Alex Zettl at UC Berkeley to develop a computational algorithm to generate well annealed polycrsytalline graphene on a computer.* This work was published in PRB. A pre-print can be found at http://arxiv.org/abs/1508.00497. Some relevant code can be found at this Github repo.*

### Size-Effect and Toughness in Quasibrittle Materials

A Statistical Mechanics Approach

Concrete — a quasibrittle material — is perhaps the most widely used material in human history. Yet, there is very limited physical understanding of the so-called “size effect” in the strength and toughness of concrete. I am building on my work on the renormalization group based approach to fracture to explain the size effect from a statistical mechanics point of view. *Some preliminary notes are available on request.*

### Renormalization Group And Fracture In Disordered Quasibrittle Materials *(Published In PRL)*

Finite-Sized Criticality

Experimental studies of fracture in quasibrittle materials such as concrete, rocks, and antler bones confirm the presence of scale invariant damage avalanches, thus indicating a continuous phase transition. However, fracture is ultimately nucleated from one dominant crack, indicating a first order transition. I, with Prof. James Sethna and Prof. Stefano Zapperi developed a scaling theory that describes this transition between first order and continuous transitions. *This work was published in PRL. A pre-print is available at http://arxiv.org/abs/1210.0989. Some relevant code can be found at this Github Repo.*

### Statistics of Brittle Fracture *(Published In PRL)*

Critical Droplet Theory

The strength of brittle materials can only be measured in a statistical sense. This is due to the fact that brittle materials are extremely sensitive to flaws, and flaws of different sizes occur in the material in a statistical manner. Powerful theorems from extreme value statistics predict that the emergent distribution of strength will not depend on the details of the flaw size distribution, and approach a universal form. We investigated the rate of convergence to the universal forms, and found that slow convergence can have real repercussions for practical applications.* This work was published in PRL. A pre-print is available at http://arxiv.org/abs/1108.4679. Some relevant code can be found at this Github Repo.*

### Dielectric Breakdown And The Metal-Insulator Transition *(Published In PRL)*

A Theory of Lightning Bolts

Experiments on the finite temperature Mott transition in VO2 films confirm the presence of critical fluctuations in the resistance jump distribution. We describe the properties of the resulting nonequilibrium metal-insulator transition and explain the universal characteristics of the resistance jump distribution. We predict that by tuning voltage, another critical point is approached, which separates a phase of boltlike avalanches from percolationlike ones. *This work was published in PRL. A pre-print is available at http://arxiv.org/abs/1009.4735*

### Improving Extreme Value Statistics *(Published in PRE)*

Transforming Tails!

The rate of convergence to the limit forms in extreme value statistics can be extremely slow, particularly for the case of the Gumbel distribution. This is essentially due to extremely rapid decay of tails of certain distributions, the Guassian being an example. We show that by applying a simple transformation to the data, the rate of convergence can be improved significantly. *This work was published in PRE. A pre-print is available at http://arxiv.org/abs/1406.3372.*