Most engineering and natural materials exhibit spatial randomness at microstructural lengthscales which significantly influence the effective macroscopic material behavior. Knowledge of this 'structure-property' relation is highly desired in engineering as it enables quantitative predictive capability to design, control, and rationally manipulate materials to address fundamental challenges in human health, energy, and resources. In my doctoral research, I focused on novel engineering materials such as nanocomposites which are poised to make aerospace structures lighter, stronger, and safer. My current work is aimed at modeling and understanding epithelial tissues for emerging bioengineering technologies such as organs-on-chips and future applications in soft robotics.
​
The central challenge in this quest is imposed by the ‘tyranny of scales’ wherein the principle physics governing the phenomena often changes as we move across scales, and so does the structure of corresponding mathematical framework. Consider the case of a biological tissue for example, to understand tissue mechanics, we go from contractile forces generated on the molecular scales, which on a cellular scale are integrated through cell-cell junctions, and these eventually give rise to tissue behavior. The situation is further complicated by the presence of several timescales from seconds to days, relevant at different lengthscales. Developing phenomenological material models of complex constitutive behaviors of such materials emerging from interplay of highly coupled physics at several spatiotemporal scales is not only a challenging task, but also a bottleneck in predictive modeling. The overarching theme of my research is to develop high-fidelity constitutive models based on a bottom up approach by connecting the microscopic and macroscopic behaviors.
Past Research
Active-superelasticity of epithelial tissues
(In collaboration with Prof. Xavier Trepat, IBEC)
We probed the constitutive behavior of epithelial tissues using a novel method to create pressurized epithelial domes of controlled shape. This 'microscopic bulge test' revealed a tensional plateau while the tissue deforms reversibly reaching up to 300% areal strains. Strikingly, barely stretched and superstretched cells (up to 1000% areal strain) coexisted within a tissue with uniform tension. These features are typical of superelastic metal alloys such as nitinol, which undergo large reversible deformations thanks to a microscopic material instability. We show that in epithelial cells, such a softening instability is triggered by stretch-induced cortical dilution, while excessive cellular deformations are arrested by network of intermediate filaments. This strain softening followed by re-stiffening at large strains results in a ‘bi-stable energy landscape of active origin’ (fig. b), which explains the tensional plateau and extreme heterogeneity in cellular strains at constant tensions. We term this behavior 'active superelasticity', which allows epithelial tissues to undergo extreme reversible deformations at nearly constant tensions.
Vertex modeling of epithelial tissues
Epithelial tissues are cellular sheets where cells are held together by adhesive cell-cell contacts mediated primarily by E-cadherin clusters. The mechanics of the epithelial cells is governed by the contractile actomyosin cortex, which is a thin meshwork of actin attached beneath the cellular membrane. These cells are organized in a polygonal tessellation in epithelia. On longer timescales, epithelial tissue looks a lot like a foam, where the surface tension in the soap films governs the foam mechanics. In epithelial, the cortical active tension plays the role of surface tension. With this analogy, vertex models for foams were adapted to model epithelial tissues in the 80s. The epithelial tissue is naturally discretized into polygons and the polygonal vertices are the degrees of freedom. The equilibrium of forces acting at these vertices due to cellular tensions then governs the epithelial behavior. Our current research is focused on developing a vertex modeling framework based on the microscopic origins of the active forces in cells.
Electrical conductivity of polymer nanocomposites
The electrical conductivity of polymers can be dramatically improved by adding negligible volume fractions of highly conductive nanofillers such as carbon nanotubes (CNTs), graphene nanoplatelets (GNPs), carbon black (CB). Conductive polymer nanocomposites are desired to be used on aircraft structures to mitigate the risk of lightning strike induced damage, for electromagnetic shielding, and for other conductive, semi-conductive, and static dissipative applications. This collaborative project is funded through the NSF Industry/University Cooperative Research Center for Novel High Voltage/Temperature Materials and Structures. We have used a tunneling-percolation model along with other analytical approaches to investigate the effect of various parameters such as size polydispersity, shape polydispersity, and filler alignment on the electrical conductivity. The model not only provided a predictive tool to be used in making better material design decisions, it also shed light on the range of applicability and accuracy of some of the frequently used analytical models.
Disorder-induced statistical effects
The interplay of disorder and long-range elastic interactions lead to interesting statistical effects such as strength-size scaling, intermittent plasticity of micro/nano-pillars, damage localization, crack surface roughness etc. Understanding such scale effects and fluctuations is of paramount importance at micro and nano scales. For example, compression experiments on micro and nano-pillars have shown intermittent accumulation of plastic strains increments. We proposed a spring lattice model which captured the intermittent plasticity accumulation following a power-law distribution with an exponent that is in excellent agreement with the mean-field theory and experiments. We also performed an extensive study of elastic-plastic-brittle transitions in disordered media and categorized elastic-plastic transition to the long-range correlated percolation class.
Scaling to RVE in composites
Of interest in applications and modeling (e.g. in stochastic finite element methods) are properties of composites not only at the representative volume element (RVE) level but also below it. This knowledge is also important when using materials at micro/nano scales, where there exist sample-to-sample fluctuations. In order to ensure a rigorous connection to micromechanics and experiments, I base my work on the Hill-Mandel condition. The highlight of our work is the scaling function that can be employed to predict the representative volume element (RVE) size for a given microstructure.