Avalanches, percolation, and stochastic damage evolution in disordered media

Disordered materials are ubiquitous in nature and engineering. The physical properties of such random heterogeneous materials are strongly coupled with the strength and spatial distribution of the disorder. Disorder leads to fluctuations in material properties which become relevant for mesoscales below the representative volume element (RVE) size. The overarching theme of this dissertation is modeling apparent properties of disordered systems on sub-RVE lengthscales using numerical techniques that are based on an explicit representation of the material microstructure. The classical picture of elastic-plastic transition as a smooth process is challenged by the compression experiments on micro/nano pillars where plastic strain was observed to accumulate intermittently. Using a discrete spring lattice modeling approach, the intermittent plastic strain avalanche behavior is well captured such that the event sizes follow a power-law distribution with an exponent that is in agreement with experiments, theory, and other models. Then using finite-size scaling analysis, the elastic-plastic transition is shown to belong to the long-range correlated percolation class, a second-order phase transition. Interestingly, this behavior is in contrast to the elastic-brittle transition in disordered media which is abrupt, akin to a first-order phase transition. The elastic-brittle transition in disordered media is characterized by foreshadowing of the final macroscopic failure by accumulation of significant amount of distributed damage which results in precursory events observed as avalanches in experiments and simulations. We use a jump Markov process to model the stochastic evolution of damage. The Markov process is informed by the avalanche size distribution for a given quasibrittle material. The fiber bundle model (FBM) is used as an example to test the viability of the proposed approach. The stochasticity and size-dependence of the damage evolution process are inherently captured through the inputs provided for the jump Markov process. The avalanche and failure strength distributions are used to describe the effect of microscopic information present in the form of the disorder on the macroscopic damage evolution behavior. We also investigated the effective thermal conductivity of spatially correlated two-phase microstructures. The presence of such spatial correlations is observed in interpenetrating phase composites (IPCs) where either phase is interconnected throughout the microstructure. A Gaussian correlation function based method is employed to generate numerical microstructures that are statistically similar to the experimentally captured micrographs. Scale-dependent bounds on the effective thermal conductivity are then obtained using the Hill-Mandel macrohomogeneity condition. A scaling function is formulated to describe the transition from statistical volume element (SVE) to representative volume element (RVE), as a function of the mesoscale, the spatial correlation length of the microstructure, the volume fraction, and the contrast between the phases. A material scaling diagram is also constructed which allows estimation of the RVE size, to within a chosen accuracy, of a given microstructure with short-range spatial correlations. Conductive polymer nanocomposites have emerged as an important class of (disordered) materials with a wide range of conductive, semiconductive, and static dissipative applications. Dramatic improvement in the electrical conductivity can be obtained by adding marginal amounts of nanofillers such as carbon nanotubes (CNTs), graphene nanoplatelets (GNPs), and carbon black (CB). This phenomenon is induced by the formation of a percolating network of nanofillers interconnected electrically by the quantum tunneling effect. A continuum percolation model along with the critical path approximation is used to investigate the effect of various filler attributes such as filler size polydispersity and alignment on the effective electrical behavior of the nanocomposite. The model proves to be an effective tool to understand the limitations of theoretical models and analyze experimental data to extract key parameters which would improve the predictive capability of this approach

Active superelasticity in three-dimensional epithelia of controlled shape

Fundamental biological processes are carried out by curved epithelial sheets that enclose a pressurized lumen. How these sheets develop and withstand three-dimensional deformations has remained unclear. Here we combine measurements of epithelial tension and shape with theoretical modelling to show that epithelial sheets are active superelastic materials. We produce arrays of epithelial domes with controlled geometry. Quantification of luminal pressure and epithelial tension reveals a tensional plateau over several-fold areal strains. These extreme strains in the tissue are accommodated by highly heterogeneous strains at a cellular level, in seeming contradiction to the measured tensional uniformity. This phenomenon is reminiscent of superelasticity, a behaviour that is generally attributed to microscopic material instabilities in metal alloys. We show that in epithelial cells this instability is triggered by a stretch-induced dilution of the actin cortex, and is rescued by the intermediate filament network. Our study reveals a type of mechanical behaviour—which we term active superelasticity—that enables epithelial sheets to sustain extreme stretching under constant tension.Peer Reviewe