https://etd.iisc.ac.in/handle/2005/40 2026-04-18T02:11:02Z https://etd.iisc.ac.in/handle/2005/2236 A 3D Lattice Model For Fracture Of Concrete : A Multiscale Approach Mungule, Mahesh Parshuram It is quite well known that fracture behavior of concrete is complex and is influenced by several factors. Apart from material properties, geometric parameters influence fracture behavior and one notable phenomenon is size effect. The existence of the size effect in concrete is well known and various attempts to model the behavior is well documented in literature. However the approach by Bazant to describe the size effect behavior in concrete has received considerable attention. The major advantage of developing the size effect law for concrete is the ability to describe the fracture behavior (namely failure strength) of large size structures inaccessible to laboratory testing. The prediction of size effect is done on the basis of laboratory testing of small size geometrically similar structures. In all the models developed earlier heterogeneity of concrete has not been quantitatively simulated. Hence, the complete description considering heterogeneity in concrete is attempted using the lattice model to understand size effect behavior in concrete. In the present study, a detailed description of the heterogeneity in concrete is at- tempted by 3D lattice structure. Analytical treatment to gain insights to fracture behavior is difficult and hence a numerical approach capable of handling the het- erogeneous nature of the material is adopted. A parametric study is performed to understand the influence of various model parameters like mesh size, failure criterion, softening model. The conventional size effect studies for 2D geometrically similar structures are performed and a comparison is done with experimentally observed behavior. The variation of fracture process zone with respect to structure size is observed as the reason for size effect. The influence of variation in properties of ag- gregate, matrix and interface are studied to explain the deviation in pre-peak and post-peak response. A statistical study is performed to establish the size dependence of linear regression parameters (Bf ‘t and D0) which are used in Bazant size effect law. An analytical framework is also proposed to substantiate the above results. Size effect in concrete is generally attributed to the effect of depth viz. the dimension in the plane of loads. However although the effect of thickness viz. a dimension in a plane perpendicular to that of the loads is not considered in concrete. The same is quite well known in fracture of metals. Therefore the variation in grading of aggregates along with the influence of thickness on fracture behavior is analysed. To understand the thickness effect a comparison of 2D and 3D geometrically similar structures is performed to understand the effect of thickness on fracture parameters. Heterogeneity is a matter of scale. A material may be homogeneous at a coarser scale while at a finer scale it is heterogeneous. Hence only way to capture the effect of the behavior at micro level on the behavior at meso level particularly in a heterogeneous material like concrete is by a multi-scale modelling. The best numerical tool for multiscale model of a heterogeneous material is lattice model. The heterogeneous nature of concrete is not just due to the presence of aggregates but is evident right from the granular characteristics of cement. The hydration of cement grain leads to the development of products with varying mechanical and chemical properties. As the micro-crack initiation and development of thermal cracking is observed at the micron level, understanding of hydration behavior in concrete can be thought of as a pre-requisite for complete understanding of fracture behavior. The properties of matrix and interface observed during hydration modelling can also be used as an input for fracture predictions at upper scale models (eg. mesoscale). This can also be used to study the coupling of scales to understand the multi-scale fracture behavior in concrete. A numerical model is hence developed to study the hydration of concrete. Due to the existence of complex mechanisms governing the hydration behavior in con- crete and the large number of parameters affecting its rate, the hydration of a grain is assumed to proceed in isolation. A single particle hydration model is developed to study the hydration of isolated grain. A shrinking core model usually used to describe the burning of coal is adopted as a base model for analytically describing the hydra- tion behavior. The shrinkage core model in literature is modified to be applicable to hydration of cement matrix. The effect of particle diameter as well as changing water concentration is incorporated into the model whereas the influence of reduction in pore sizes as well as the effect due to embedding of particles and the constraint due to hydration of neighbouring particles is accounted using correction factor. The effect of temperature on rate of hydration is considered to be independent of the physical and chemical aspects of grain. Hence a temperature function developed using Arrhe- nius equation and activation energy is incorporated separately. The porous nature of reaction products affects the diffusivity leading to the development of tortuous path for flow of water through the hydrated portion. Knowing the tortuosity it is possible to obtain the diffusivity which in turn can be used as an input to the lattice model. An algorithm is developed to determine the tortuosity in diffusion of water through the reaction products. The tortuosity depends on the distribution of pores in the hydrated system. This requires the use of simulation technique to generate the initial position of voids. A simulation technique is also required to generate the initial con- figuration of hydrating cement system. In order to generate the initial configurations of such systems a numerical technique to generate a large scale assembly of particles is proposed. In the present work, parameters of Bazant's size effect law Bf’t and D0 are shown to depend on structure size and heterogeneity. The span to thickness ratio of the structure increases fracture energy and also substantially influences the response of structure. The variation in failure load occurring due to the heterogeneous nature of the material is shown to follow a normal distribution. The fracture behavior of a material is seen to be influenced strongly by the variation in the strength of matrix and interface. The model proposed to describe the hydration process of cement can be used to determine the properties of matrix and interface. The degree of hydration as well as the embedded centre plane area can be adopted as a measure of strength of matrix and interface. The understanding of the hydration process and the wall effect around the aggregate surface can possibly improve our ability to predict the strength of interface. The material strength of the interface is certainly a necessary input to the lattice model. Infact experimental determination of interface strength is a lot more complicated than the present numerical approach. The only weakness of the present numerical approach is the assumption regarding certain empirical constants which of course may be improved further. Understanding of material behavior can be further improved if a molecular dynamics approach is adopted to describe the hydration behavior of cement. The approach via molecular dynamics is suggested as a problem for future research. 2013-09-10T00:00:00Z https://etd.iisc.ac.in/handle/2005/5218 Adaptive reduced order modeling of dynamical systems through novel a posteriori error estimators : Application to uncertainty quantification Hossain, Md Nurtaj Multi-query problems such as uncertainty quantification, optimization of a dynamical system require solving a governing differential equation at multiple parameter values. Therefore, for large systems, the computational cost becomes prohibitive. Replacing the original discretized higher dimensional model with a faster reduced order model (ROM) can alleviate this computationally prohibitive task significantly. However, a ROM incurs error in the solution due to approximation in a lower dimensional subspace. Moreover, ROMs lack robustness in terms of effectiveness over the entire parameter range. Accordingly, often they are classified as local and global, based on their construction in the parametric domain. Availability of an error bound or error estimator of a ROM helps in achieving this robustness, mainly by allowing adaptivity. The goal of this thesis is to propose such error estimators and use them to develop adaptive proper orthogonal decomposition-based ROM for uncertainty quantification. Therefore, two a posteriori error estimators, one for linear and another for nonlinear dynamical system, respectively, are developed based on the residual in the differential equation. To develop an a posteriori error estimator for nonlinear systems, first, an upper bound on the norm of the state transition matrix is derived and then it is used to develop the error estimator. Numerically they are compared with the error estimators available in the current literature. This comparison revealed that the proposed estimators follow the trend of the exact error more closely, thus serving as an improvement over the state-of-the-art. These error estimators are used in conjunction with a greedy search to develop adaptive algorithms for the construction of robust ROM. The adaptively trained ROM is subsequently deployed for uncertainty quantification by invoking it in a statistical simulation. For the linear dynamical system, two algorithms are proposed for building robust ROMs --- one for local, and another for global. For the nonlinear dynamical system, an adaptive algorithm is developed for the global ROM. In the training stage of global ROM, a modification is proposed --- at each iteration of the greedy search, the ROM is trained at a few local maxima in addition to the global maxima of the error estimator --- leading to an accelerated convergence. For this purpose, a multi-frequency vibrational particle swarm optimization is employed. It is shown that the proposed algorithm for adaptive training of ROMs poses ample scope of parallelization. Different numerical studies: (i) bladed disk assembly, (ii) Burgers' equation, and (iii) beam on nonlinear Winkler foundation, are performed to test the efficiency of the error estimators and the accuracy achieved by the modified greedy search. A speed-up of more than two orders of magnitude is achieved using the ROM, trained with the proposed algorithm, and error estimators. However, adaptive training of ROM is also expensive due to multiple evaluations of HDM. To address this issue, a novel random excitation-based training is proposed in this thesis. Accordingly, depending upon the parameter range of interest, bandlimited random white noise excitations are chosen and the ROM is trained from the corresponding responses. This is applied to linear and nonlinear vibrating systems with spatial periodicity and imperfection. From the numerical studies, it is found that the proposed method reduces the cost of training significantly, and successfully captures the behavior such as alternate pass- and stop-bands of vibration propagation, peak response. https://etd.iisc.ac.in/handle/2005/8139 Advanced Thermomechanical Modeling of Soft Matter Systems Raza, Asif This thesis deals with advanced thermomechanical modeling of complex soft matter systems, including polymers, gels, and biological tissues. It addresses a few fundamental limitations of classical theories, such as the paradox of infinite heat propagation speed and insufficient microstructural insights from the classical fluctuation theory, by employing geometric and non-Fourier approaches. The thesis is structured around three core contributions. The first explores strain-induced crystallization (SIC) in polymers using Ruppeiner’s geometric thermodynamics. This approach reveals a "spurious isochoric energy" originating from the conformational stretching of already crystallized segments, an unphysical component attributed to considering the crystallized manifold as Euclidean. By analyzing scalar curvature and critical thermodynamic states, the work proposes a modified free energy formulation that eliminates this spurious energy, leading to accurate stress recovery and a more physically consistent constitutive theory for SIC. The second part applies geometric thermodynamics to analyze the volumetric phase transition in polyacrylamide gels. Utilizing a Landau-Ginzburg type free energy functional in conjunction with Flory-Huggins theory, the scalar curvature is employed to gain insights into the evolving microstructure. Divergence in curvature at critical points is directly linked to the divergence of correlation length, indicating a heterogeneous microstructure during phase transition and supporting experimental observations of phase segregation. The study also confirms the universality class of the gel's phase transition, aligning it with van der Waals fluids and black hole systems. A proposed modification to the free energy addresses unphysical nonconvexity, negating the need for Maxwell construction. The final contribution presents a robust two-dimensional finite element framework for small-strain coupled thermoelasticity, incorporating both classical Fourier and Dual-Phase-Lag (DPL) heat conduction models. This framework is rigorously validated against experimental data for processed bologna meat, conclusively demonstrating the DPL model's superior predictive capability in capturing finite speed of thermal signal propagation and wave-like heat transfer phenomena. The DPL model accurately predicts delayed onset, sharper transitions, and localized stress amplification in response to rapid thermal fronts and wave superposition effects, offering a more realistic representation of thermoelastic stress and strain fields compared to the Fourier model. Overall, this thesis advances the understanding and modeling of soft matter systems under diverse thermal and mechanical conditions. It underscores the critical role of advanced, non-classical thermodynamic and heat conduction theories in accurately predicting material behavior and extracting crucial microstructural information, offering valuable insights for applications in bioengineering, materials science, and food processing. Future work is outlined to extend these methodologies to more complex geometries, large deformations, anisotropic and temperature-dependent material properties, and to explore inverse problems for parameter identification. https://etd.iisc.ac.in/handle/2005/6407 Aggregate and Disaggregate-level Models of Public Transit Ridership in Bengaluru, India Deepa, L Ridership forecasting models are valuable tools for public transit agencies to assess and quantify the possible impacts of their operational strategies and service improvements on transit demand and revenue. Although a rich body of literature exists on this topic, there has not been much study on transit ridership forecasting for cities in emerging economies such as India. Further, the literature in this area is saddled with one or more of the following methodological and substantive issues: (a) the difficulty of relating spatially aggregate demand data (typically available with transit agencies) to disaggregate, transit stop-level catchment characteristics, (b) inadequate consideration of inter-route interactions such as competition and complementarity for transit riders, (c) neglect of the endogeneity and nonlinearity of the influence of service frequency on ridership, (d) ad-hoc ways to address the overlapping of catchment areas among closely spaced stops, (e) inadequate efforts toward quantifying the impact of service reliability on ridership and revenue, and (f) limited efforts on understanding the role of subjective perceptions of service quality on transit usage (and the extent of usage). The overarching goal of this dissertation is to advance the formulation of bus transit ridership models to address the methodological and substantive issues discussed above. To this end, first, the study develops a direct demand modeling framework for forecasting bus transit ridership at a spatially disaggregate stop-route level. The proposed model is applied to a rich empirical dataset put together from various sources, including the bus ticket sales and service data from Bengaluru Metropolitan Transport Corporation (BMTC). Empirical findings from the model indicate that while service frequency is one of the significant drivers of transit ridership even after controlling for endogeneity, routes with low current frequency (1 to 3 buses per hour) in Bengaluru benefit the most from increasing frequency than those with high current frequency. In addition, the results suggest that ignoring endogeneity between service frequency and ridership would result in overestimating the impact of service frequency on ridership. Next, the study expands the above direct demand modeling framework to examine both theoretically and empirically the relationships between transit ridership, service frequency (or headways), and service variability (variability in headways) using a tri-variate equations framework that considers endogeneity relationships between demand and supply. In addition, auxiliary supply models are developed to understand the determinants of service frequency and service variability in Bengaluru. The proposed models are applied for policy analyses to quantify the ridership impacts of service modification strategies, such as an increase in service frequency and an improvement in service reliability, on bus transit ridership in Bengaluru. Empirical results from these models demonstrate that headway variability negatively impacts transit ridership and passenger-kilometres, with the adverse effect exacerbating as variability increases. This trend is in contrast to the diminishing benefits of increasing service frequency at high current frequency levels. Further, the empirical results and policy simulations indicate that transit agencies can potentially gain greater ridership and revenue if they can lower headway variability rather than by merely adding more buses to high-frequency routes. Finally, the study develops a disaggregate, integrated choice and latent variable model of individual-level transit usage and extent of usage to complement the direct demand modeling frameworks discussed above. Specifically, the model considers the influence of individuals’ demographics and their subjective perceptions of transit service quality on the usage and extent of usage of bus transit. The role of subjective perceptions is incorporated using a generalized heterogeneous data modeling framework that treats individuals’ perceptions as latent explanatory variables identified using Likert scale measurements of the perceptions. In doing so, the study addresses the methodological issue of disentangling individuals’ unfamiliarity from their informed opinions underlying the Likert scale measurements of individuals’ subjective perceptions. The proposed model is applied to examine individuals’ transit usage and the extent of usage using empirical data from Bengaluru, India. The empirical results shed light on the role of individuals’ demographic characteristics and perceptions of transit service quality on their usage and extent of usage of bus transit in Bengaluru. Additionally, comparing the empirical model with another model that did not consider individuals’ unfamiliarity with transit service highlighted the importance of separating the influence of unfamiliarity from that of informed perceptions of service quality on transit usage. To the best of our knowledge, this dissertation is the first attempt to (a) develop a comprehensive demand modeling framework for analyzing bus transit ridership in an Indian city using empirical data from a large-scale transit system, (b) address several methodological and substantive issues identified in existing bus transit ridership studies, (c) examine both theoretically and empirically the endogeneity and non-linear effects of two important transit service attributes – service frequency and variability in headways – on demand for public transit, (d) shed light on individuals’ use and extent of use of bus transit in an Indian city while also focusing on the role of their subjective perceptions, and (e) address the issue of separating unfamiliarity from informed opinions when analyzing the role of subjective perceptions on individuals’ transit usage. Although the application of the models in this dissertation is for Bengaluru, the proposed methodological frameworks and empirical strategies are potentially applicable for studying bus transit demand in other cities in India and other countries. Specifically, the models can be used as descriptive tools to understand the factors that influence bus transit ridership, and as predictive tools to forecast bus ridership in response to a variety of what-if scenarios of interest to transit agencies – as long as empirical parameters are estimated using relevant data from the city of interest. In this context, it will be useful to apply the models to other cities to examine their applicability and the generalizability of substantive findings.