+publisher:"Indian Institute of Science" +contributor:("Roy, Debasish")

Indian Institute of Science

1. Devaraj, G. Schemes for Smooth Discretization And Inverse Problems - Case Study on Recovery of Tsunami Source Parameters.

Degree: PhD, Faculty of Engineering, 2017, Indian Institute of Science

URL: http://etd.iisc.ac.in/handle/2005/2719

► This thesis deals with smooth discretization schemes and inverse problems, the former used in efficient yet accurate numerical solutions to forward models required in turn… (more)

▼ This thesis deals with smooth discretization schemes and inverse problems, the former used in efficient yet accurate numerical solutions to forward models required in turn to solve inverse problems. The aims of the thesis include, (i) development of a stabilization techniques for a class of forward problems plagued by unphysical oscillations in the response due to the presence of jumps/shocks/high gradients, (ii) development of a smooth hybrid discretization scheme that combines certain useful features of Finite Element (FE) and Mesh-Free (MF) methods and alleviates certain destabilizing factors encountered in the construction of shape functions using the polynomial reproduction method and, (iii) a first of its kind attempt at the joint inversion of both static and dynamic source parameters of the 2004 Sumatra-Andaman earthquake using tsunami sea level anomaly data. Following the introduction in Chapter 1 that motivates and puts in perspective the work done in later chapters, the main body of the thesis may be viewed as having two parts, viz., the first part constituting the development and use of smooth discretization schemes in the possible presence of destabilizing factors (Chapters 2 and 3) and the second part involving solution to the inverse problem of tsunami source recovery (Chapter 4). In the context of stability requirements in numerical solutions of practical forward problems, Chapter 2 develops a new stabilization scheme. It is based on a stochastic representation of the discretized field variables, with a view to reduce or even eliminate unphysical oscillations in the MF numerical simulations of systems developing shocks or exhibiting localized bands of extreme plastic deformation in the response. The origin of the stabilization scheme may be traced to nonlinear stochastic filtering and, consistent with a class of such filters, gain-based additive correction terms are applied to the simulated solution of the system, herein achieved through the Element-Free Galerkin (EFG) method, in order to impose a set of constraints that help arresting the spurious oscillations. The method is numerically illustrated through its application to a gradient plasticity model whose response is often characterized by a developing shear band as the external load is gradually increased. The potential of the method in stabilized yet accurate numerical simulations of such systems involving extreme gradient variations in the response is thus brought forth. Chapter 3 develops the MF-based discretization motif by balancing this with the widespread adoption of the FE method. Thus it concentrates on developing a 'hybrid' scheme that aims at the amelioration of certain destabilizing algorithmic issues arising from the necessary condition of moment matrix invertibility en route to the generation of smooth shape functions. It sets forth the hybrid discretization scheme utilizing bivariate simplex splines as kernels in a polynomial reproducing approach adopted over a conventional FE-like domain discretization based on Delaunay… Advisors/Committee Members: Roy, Debasish (advisor).

Subjects/Keywords: Smooth Discretization; Inverse Geodetic Problems; Strain Gradient Platicity Systems; Polynomial Reproducing Simplex Splines; Earthquake Source Parameters; Sumatra-Andaman Earthquake Source Parameters-2004; Tsunami Source Recovery; Tsunami Numerical Modeling; Polynomial Shape Functions; Mesh Free Method; Finite Element Method; Inverse Problems; Civil Engineering

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APA (6^th Edition):

Devaraj, G. (2017). Schemes for Smooth Discretization And Inverse Problems - Case Study on Recovery of Tsunami Source Parameters. (Doctoral Dissertation). Indian Institute of Science. Retrieved from http://etd.iisc.ac.in/handle/2005/2719

Chicago Manual of Style (16^th Edition):

Devaraj, G. “Schemes for Smooth Discretization And Inverse Problems - Case Study on Recovery of Tsunami Source Parameters.” 2017. Doctoral Dissertation, Indian Institute of Science. Accessed March 08, 2021. http://etd.iisc.ac.in/handle/2005/2719.

MLA Handbook (7^th Edition):

Devaraj, G. “Schemes for Smooth Discretization And Inverse Problems - Case Study on Recovery of Tsunami Source Parameters.” 2017. Web. 08 Mar 2021.

Vancouver:

Devaraj G. Schemes for Smooth Discretization And Inverse Problems - Case Study on Recovery of Tsunami Source Parameters. [Internet] [Doctoral dissertation]. Indian Institute of Science; 2017. [cited 2021 Mar 08]. Available from: http://etd.iisc.ac.in/handle/2005/2719.

Council of Science Editors:

Devaraj G. Schemes for Smooth Discretization And Inverse Problems - Case Study on Recovery of Tsunami Source Parameters. [Doctoral Dissertation]. Indian Institute of Science; 2017. Available from: http://etd.iisc.ac.in/handle/2005/2719

Indian Institute of Science

2. Rajathachal, Karthik M. Application Of Polynomial Reproducing Schemes To Nonlinear Mechanics.

Degree: MSc Engg, Faculty of Engineering, 2011, Indian Institute of Science

URL: http://etd.iisc.ac.in/handle/2005/1093

► The application of polynomial reproducing methods has been explored in the context of linear and non linear problems. Of specific interest is the application of… (more)

▼ The application of polynomial reproducing methods has been explored in the context of linear and non linear problems. Of specific interest is the application of a recently developed reproducing scheme, referred to as the error reproducing kernel method (ERKM), which uses non-uniform rational B-splines (NURBS) to construct the basis functions, an aspect that potentially helps bring in locall support, convex approximation and variation diminishing properties in the functional approximation. Polynomial reproducing methods have been applied to solve problems coming under the class of a simplified theory called Cosserat theory. Structures such as a rod which have special geometric properties can be modeled with the aid of such simplified theories. It has been observed that the application of mesh-free methods to solve the aforementioned problems has the advantage that large deformations and exact cross-sectional deformations in a rod could be captured exactly by modeling the rod just in one dimension without the problem of distortion of elements or element locking which would have had some effect if the problem were to be solved using mesh based methods. Polynomial reproducing methods have been applied to problems in fracture mechanics to study the propagation of crack in a structure. As it is often desirable to limit the use of the polynomial reproducing methods to some parts of the domain where their unique advantages such as fast convergence, good accuracy, smooth derivatives, and trivial adaptivity are beneficial, a coupling procedure has been adopted with the objective of using the advantages of both FEM and polynomial reproducing methods. Exploration of SMW (Sherman-Morrison-Woodbury) in the context of polynomial reproducing methods has been done which would assist in calculating the inverse of a perturbed matrix (stiffness matrix in our case). This would to a great extent reduce the cost of computation. In this thesis, as a first step attempts have been made to apply Mesh free cosserat theory to one dimensional problems. The idea was to bring out the advantages and limitations of mesh free cosserat theory and then extend it to 2D problems. Advisors/Committee Members: Roy, Debasish (advisor).

Subjects/Keywords: Crack Resistance; Crack Propagation; Polynomial Equation; Mesh Free Method (Mechanics); Cosserat Rod Model; Error Reproducing Kernel Method; Cosserat Theory; Nonlinear Mechanics; Applied Mechanics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Rajathachal, K. M. (2011). Application Of Polynomial Reproducing Schemes To Nonlinear Mechanics. (Masters Thesis). Indian Institute of Science. Retrieved from http://etd.iisc.ac.in/handle/2005/1093

Chicago Manual of Style (16^th Edition):

Rajathachal, Karthik M. “Application Of Polynomial Reproducing Schemes To Nonlinear Mechanics.” 2011. Masters Thesis, Indian Institute of Science. Accessed March 08, 2021. http://etd.iisc.ac.in/handle/2005/1093.

MLA Handbook (7^th Edition):

Rajathachal, Karthik M. “Application Of Polynomial Reproducing Schemes To Nonlinear Mechanics.” 2011. Web. 08 Mar 2021.

Vancouver:

Rajathachal KM. Application Of Polynomial Reproducing Schemes To Nonlinear Mechanics. [Internet] [Masters thesis]. Indian Institute of Science; 2011. [cited 2021 Mar 08]. Available from: http://etd.iisc.ac.in/handle/2005/1093.

Council of Science Editors:

Rajathachal KM. Application Of Polynomial Reproducing Schemes To Nonlinear Mechanics. [Masters Thesis]. Indian Institute of Science; 2011. Available from: http://etd.iisc.ac.in/handle/2005/1093

Indian Institute of Science

3. Khatri, Vikash. A Smooth Finite Element Method Via Triangular B-Splines.

Degree: MSc Engg, Faculty of Engineering, 2013, Indian Institute of Science

URL: http://etd.iisc.ac.in/handle/2005/2155

► A triangular B-spline (DMS-spline)-based finite element method (TBS-FEM) is proposed along with possible enrichment through discontinuous Galerkin, continuous-discontinuous Galerkin finite element (CDGFE) and stabilization techniques.… (more)

▼ A triangular B-spline (DMS-spline)-based finite element method (TBS-FEM) is proposed along with possible enrichment through discontinuous Galerkin, continuous-discontinuous Galerkin finite element (CDGFE) and stabilization techniques. The developed schemes are also numerically explored, to a limited extent, for weak discretizations of a few second order partial differential equations (PDEs) of interest in solid mechanics. The presently employed functional approximation has both affine invariance and convex hull properties. In contrast to the Lagrangian basis functions used with the conventional finite element method, basis functions derived through n-th order triangular B-splines possess (n ≥ 1) global continuity. This is usually not possible with standard finite element formulations. Thus, though constructed within a mesh-based framework, the basis functions are globally smooth (even across the element boundaries). Since these globally smooth basis functions are used in modeling response, one can expect a reduction in the number of elements in the discretization which in turn reduces number of degrees of freedom and consequently the computational cost. In the present work that aims at laying out the basic foundation of the method, we consider only linear triangular B-splines. The resulting formulation thus provides only a continuous approximation functions for the targeted variables. This leads to a straightforward implementation without a digression into the issue of knot selection, whose resolution is required for implementing the method with higher order triangular B-splines. Since we consider only n = 1, the formulation also makes use of the discontinuous Galerkin method that weakly enforces the continuity of first derivatives through stabilizing terms on the interior boundaries. Stabilization enhances the numerical stability without sacrificing accuracy by suitably changing the weak formulation. Weighted residual terms are added to the variational equation, which involve a mesh-dependent stabilization parameter. The advantage of the resulting scheme over a more traditional mixed approach and least square finite element is that the introduction of additional unknowns and related difficulties can be avoided. For assessing the numerical performance of the method, we consider Navier’s equations of elasticity, especially the case of nearly-incompressible elasticity (i.e. as the limit of volumetric locking approaches). Limited comparisons with results via finite element techniques based on constant-strain triangles help bring out the advantages of the proposed scheme to an extent. Advisors/Committee Members: Roy, Debasish (advisor).

Subjects/Keywords: Finite Element Method (FEM); B-Splines; Triangular B-Splines; Continuous Galerkin Finite Element Method; Continuous-Discontinuous Galerkin Finite Element Method; Civil Engineering

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Khatri, V. (2013). A Smooth Finite Element Method Via Triangular B-Splines. (Masters Thesis). Indian Institute of Science. Retrieved from http://etd.iisc.ac.in/handle/2005/2155

Chicago Manual of Style (16^th Edition):

Khatri, Vikash. “A Smooth Finite Element Method Via Triangular B-Splines.” 2013. Masters Thesis, Indian Institute of Science. Accessed March 08, 2021. http://etd.iisc.ac.in/handle/2005/2155.

MLA Handbook (7^th Edition):

Khatri, Vikash. “A Smooth Finite Element Method Via Triangular B-Splines.” 2013. Web. 08 Mar 2021.

Vancouver:

Khatri V. A Smooth Finite Element Method Via Triangular B-Splines. [Internet] [Masters thesis]. Indian Institute of Science; 2013. [cited 2021 Mar 08]. Available from: http://etd.iisc.ac.in/handle/2005/2155.

Council of Science Editors:

Khatri V. A Smooth Finite Element Method Via Triangular B-Splines. [Masters Thesis]. Indian Institute of Science; 2013. Available from: http://etd.iisc.ac.in/handle/2005/2155

Indian Institute of Science

4. Deepu, S P. Non-Local Continuum Models for Damage in Solids and Delamination of Composites.

Degree: PhD, Engineering, 2019, Indian Institute of Science

URL: http://etd.iisc.ac.in/handle/2005/4206

► The focus of the thesis is on developing new damage models for brittle materials and using these to study delamination of composite structures. Chapter 1… (more)

▼ The focus of the thesis is on developing new damage models for brittle materials and using these to study delamination of composite structures. Chapter 1 gives an introductory literature review in order to motivate the work undertaken in the chapters to follow. Chapter 2 deals with a new micropolar damage model for delamination in composites. By combining phase field theory and peridynamics, Chapter 3 develops a new formalism to study damage in brittle materials under dynamic loading. Chapter 4 exploits and extends this idea for modelling delamination of composites. An extended chapter-wise summary of the contributions in the thesis is provided below. In Chapter 2, a micropolar cohesive damage model for delamination of composites is proposed. The main idea is to embed micropolarity, which brings in an added layer of kinematics through the micro-rotation degrees of freedom within a continuum model to account for the micro-structural effects during delamination. The resulting cohesive model, described through a modified traction separation law, includes micro-rotational jumps in addition to displacement jumps across the interface. The incorporation of micro-rotation requires the model to be supplemented with physically relevant material length scale parameters, whose effects during delamination in modes I and II are brought forth using numerical simulations appropriately supported by experimental evidences. In Chapter 3, we attempt at reformulating the phase field theory within the framework of peridynamics (PD) to arrive at a non-local continuum damage model. This obtains a better criterion for bond breaking in PD, marking a departure from the inherently ad-hoc bond-stretch-based or bond-energy-based conditions and thus allowing the model to simulate fragmentation which a phase field model cannot by itself accomplish. Moreover, posed within the PD setup, the integral equation for the phase field eases the smoothness restrictions on the field variable. Taking advantages of both the worlds, the scheme thus offers a better computational approach to problems involving cracks or discontinuities. Starting with Hamilton’s principle, an equation of the Ginzburg-Landau type with dissipative correction is arrived at as a model for the phase field evolution. A constitutive correspondence route is followed to incorporate classical constitutive relations within our PD model. Numerical simulations of dynamic crack propagation (including branching) and the Kalthoff-Winkler experiment are also provided. To demonstrate the natural ability of the model to prevent interpenetration, a mode II delamination simulation is presented. A brief discussion on the convergence of PD equations to classical theory is provided in the Appendix B. In Chapter 4, we extend and exploit the phase field based PD damage model, developed in Chapter 3, for studying delamination of composites. Utilizing the phase field augmented PD framework, our idea is to model the interfacial cohesive damage through degradation functions and the fracture or… Advisors/Committee Members: Roy, Debasish (advisor).

Subjects/Keywords: Micropolar Theory; Peridynamics Damage Model; Phase Field Theory; Micropolar Delamination Model; Cohesive Zone Model (CZM); Delamination of Composites; Cohesive Zone Modelling; Micropolar Cohesive Damage Model; Peridynamics; Civil Engineering

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Deepu, S. P. (2019). Non-Local Continuum Models for Damage in Solids and Delamination of Composites. (Doctoral Dissertation). Indian Institute of Science. Retrieved from http://etd.iisc.ac.in/handle/2005/4206

Chicago Manual of Style (16^th Edition):

Deepu, S P. “Non-Local Continuum Models for Damage in Solids and Delamination of Composites.” 2019. Doctoral Dissertation, Indian Institute of Science. Accessed March 08, 2021. http://etd.iisc.ac.in/handle/2005/4206.

MLA Handbook (7^th Edition):

Deepu, S P. “Non-Local Continuum Models for Damage in Solids and Delamination of Composites.” 2019. Web. 08 Mar 2021.

Vancouver:

Deepu SP. Non-Local Continuum Models for Damage in Solids and Delamination of Composites. [Internet] [Doctoral dissertation]. Indian Institute of Science; 2019. [cited 2021 Mar 08]. Available from: http://etd.iisc.ac.in/handle/2005/4206.

Council of Science Editors:

Deepu SP. Non-Local Continuum Models for Damage in Solids and Delamination of Composites. [Doctoral Dissertation]. Indian Institute of Science; 2019. Available from: http://etd.iisc.ac.in/handle/2005/4206

Indian Institute of Science

5. Chowdhury, Shubhankar Roy. Non-classical mechanics and thermodynamics for continuum modelling of solids.

Degree: PhD, Engineering, 2019, Indian Institute of Science

URL: http://etd.iisc.ac.in/handle/2005/4193

► This thesis dwells upon several aspects of continuum mechanics and thermodynamics to model elastic and inelastic response of solids. Broadly, the work presented may be… (more)

▼ This thesis dwells upon several aspects of continuum mechanics and thermodynamics to model elastic and inelastic response of solids. Broadly, the work presented may be categorized into two parts{ one focusing on the development of generalized continuum description in the context of elastic materials and the other on the thermodynamics of dissipative processes whilst considering, in some detail, the physics of deformation too. The first part begins with the proposal for a state-based micropolar peridynamic theory for linear elastic solids. The main motivation is to introduce additional micro-rotational degrees of freedom to each material point and thus naturally bring in the physically relevant material length scale parameters into peridynamics. Non-ordinary type modelling via constitutive correspondence is adopted here to de ne the micropolar peridynamic material. Along with a general three-dimensional model, homogenized one dimensional Timoshenko type beam models for both the proposed micropolar and the standard non-polar peridynamic variants are derived. The efficacy of the proposed models in analyzing continua with length scale effects is established via numerical simulations of a few beam and plane-stress problems. Continuing with our e ort in developing homogenized reduced dimensional models, a state-based peridynamic formulation for linear elastic shells is presented next. The emphasis is on introducing, perhaps for the first time, a general surface based peridynamic model to represent the deformation characteristics of structures that have one geometric dimension much smaller than the other two. A new notion of curved bonds is exploited to model force transfer between the peridynamic particles describing the shell. Starting with the three dimensional force and deformation states, appropriate surface based force, moment and several deformation states are arrived at. Upon application on the curved bonds, such states yield the necessary force and deformation vectors governing the motion of the shell. The peridynamic shell theory is numerically assessed against simulations on static deformation of spherical and cylindrical shells and those on at plates. As a transition to the second part of the thesis, our next work shares features of the first part (micropolarity and homogenization) as well as the second (equation with viscous force, i.e., dissipative process). Starting with a micropolar formulation, known to account for nonlocal microstructural effects at the continuum level, a generalized Langevin equation (GLE) for a particle, describing the predominant motion of a localized region through a single displacement degree-of-freedom, is derived. The GLE features a memory dependent multiplicative or internal noise, which appears upon recognising that the micro-rotation variables possess randomness owing to an uncertainty principle. Unlike its classical version, the new GLE qualitatively reproduces the experimentally measured fluctuations in the steady-state mean square displacement of scattering centers in a… Advisors/Committee Members: Roy, Debasish (advisor).

Subjects/Keywords: Elastic Solids; Inelastic response; Solids; Linear elastic solids; Modelling; Brittle damage; Research Subject Categories::TECHNOLOGY::Civil engineering and architecture::Other civil engineering and architecture

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Chowdhury, S. R. (2019). Non-classical mechanics and thermodynamics for continuum modelling of solids. (Doctoral Dissertation). Indian Institute of Science. Retrieved from http://etd.iisc.ac.in/handle/2005/4193

Chicago Manual of Style (16^th Edition):

Chowdhury, Shubhankar Roy. “Non-classical mechanics and thermodynamics for continuum modelling of solids.” 2019. Doctoral Dissertation, Indian Institute of Science. Accessed March 08, 2021. http://etd.iisc.ac.in/handle/2005/4193.

MLA Handbook (7^th Edition):

Chowdhury, Shubhankar Roy. “Non-classical mechanics and thermodynamics for continuum modelling of solids.” 2019. Web. 08 Mar 2021.

Vancouver:

Chowdhury SR. Non-classical mechanics and thermodynamics for continuum modelling of solids. [Internet] [Doctoral dissertation]. Indian Institute of Science; 2019. [cited 2021 Mar 08]. Available from: http://etd.iisc.ac.in/handle/2005/4193.

Council of Science Editors:

Chowdhury SR. Non-classical mechanics and thermodynamics for continuum modelling of solids. [Doctoral Dissertation]. Indian Institute of Science; 2019. Available from: http://etd.iisc.ac.in/handle/2005/4193

Indian Institute of Science

6. Narayan, Shashi. Smooth Finite Element Methods with Polynomial Reproducing Shape Functions.

Degree: MSc Engg, Faculty of Engineering, 2018, Indian Institute of Science

URL: http://etd.iisc.ac.in/handle/2005/3332

► A couple of discretization schemes, based on an FE-like tessellation of the domain and polynomial reproducing, globally smooth shape functions, are considered and numerically explored… (more)

Subjects/Keywords: Finite Element Methods; Smooth Finite Element Methods; Polynomial Reproducing Shape Functions; Globally Smooth Space Functions; DMS-FEM (Tetrahedral B Splines-Finite Element Method) Shape Functions; Plate Bending Models; Mindlin Plate Bending; Simplex Splines; Mesh-Free Shape Functions; Tetrahedral B Splines (DMS); Mesh-free Methods; Civil Engineering

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Narayan, S. (2018). Smooth Finite Element Methods with Polynomial Reproducing Shape Functions. (Masters Thesis). Indian Institute of Science. Retrieved from http://etd.iisc.ac.in/handle/2005/3332

Chicago Manual of Style (16^th Edition):

Narayan, Shashi. “Smooth Finite Element Methods with Polynomial Reproducing Shape Functions.” 2018. Masters Thesis, Indian Institute of Science. Accessed March 08, 2021. http://etd.iisc.ac.in/handle/2005/3332.

MLA Handbook (7^th Edition):

Narayan, Shashi. “Smooth Finite Element Methods with Polynomial Reproducing Shape Functions.” 2018. Web. 08 Mar 2021.

Vancouver:

Narayan S. Smooth Finite Element Methods with Polynomial Reproducing Shape Functions. [Internet] [Masters thesis]. Indian Institute of Science; 2018. [cited 2021 Mar 08]. Available from: http://etd.iisc.ac.in/handle/2005/3332.

Council of Science Editors:

Narayan S. Smooth Finite Element Methods with Polynomial Reproducing Shape Functions. [Masters Thesis]. Indian Institute of Science; 2018. Available from: http://etd.iisc.ac.in/handle/2005/3332

Indian Institute of Science

7. Rahaman, Md Masiur. Dynamic Flow Rules in Continuum Visco-plasticity and Damage Models for Poly-crystalline Solids.

Degree: PhD, Faculty of Science, 2019, Indian Institute of Science

URL: http://etd.iisc.ac.in/handle/2005/4240

► Modelling highly non-linear, strongly temperature- and rate-dependent visco-plastic behaviour of poly-crystalline solids (e.g., metals and metallic alloys) is one of the most challenging topics of… (more)

▼ Modelling highly non-linear, strongly temperature- and rate-dependent visco-plastic behaviour of poly-crystalline solids (e.g., metals and metallic alloys) is one of the most challenging topics of contemporary research interest, mainly owing to the increasing use of metallic structures in engineering applications. Numerous classical models have been developed to model the visco-plastic behaviour of poly-crystalline solids. However, limitations of classical visco-plasticity models have been realized mainly in two cases: in problems at the scale of mesoscopic length (typically in the range of a tenth of a micron to a few tens of micron) or lower, and in impact problems under high-strain loading with varying temperature. As a remedy of the first case, several length scale dependent non-local visco-plasticity models have been developed in the last few decades. Unfortunately, a rationally grounded continuum model with the capability of reproducing visco-plastic response in accord with the experimental observations under high strain-rates and varying temperatures remains elusive and attempts in this direction are often mired in controversies. With the understanding of metal visco-plasticity as a macroscopic manifestation of the underlying dislocation motion, there are attempts to develop phenomenological as well as physics-based continuum models that could be applied across different regimes of temperature and strain rate. Yet, none of these continuum visco-plasticity models accurately capture the experimentally observed oscillations in the stress-strain response of metals (e.g. molybdenum, tantalum etc.) under high strain rates and such phenomena are sometimes even dismissed as mere experimental artefacts. The question arises as to whether the existing models have consistently overlooked any important mechanism related to dislocation motion which could be very important at high strain-rate loading and possibly responsible for oscillations in the stress-strain response. In the search for an answer to this question, one observes that the existing macro-scale continuum visco-plasticity models do not account for the effects of dislocation inertia which is identified in this thesis as a dominating factor in the visco-plastic response under high strain rates. Incorporating the effect of dislocation inertia in the continuum response, a visco-plasticity model is developed. Here the ow rule is derived based on an additional balance law, the micro-force balance, for the forces arising from (and maintaining) the plastic flow. The micro-force balance together with the classical momentum balance equations thus describes the visco-plastic response of isotropic poly-crystalline materials. The model is thermodynamically consistent as the constitutive relations for the fluxes are determined on satisfying the laws of thermodynamics. The model includes consistent derivation of temperature evolution, thus replaces the empirical route. Partial differential equations (PDEs) describing the visco-plastic behaviour in the present model is… Advisors/Committee Members: Roy, Debasish (advisor).

Subjects/Keywords: Visco-plasticity Model; Visco-plastic Damage Model; Polycrystalline Solids; Thermo-viscoplastic Damage Model; Micro-inertia Driven Flow Rule; Peridynamics Model; Smooth Particle Hydrodynamics (SPH); Dynamic Flow Rule; Mathematics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Rahaman, M. M. (2019). Dynamic Flow Rules in Continuum Visco-plasticity and Damage Models for Poly-crystalline Solids. (Doctoral Dissertation). Indian Institute of Science. Retrieved from http://etd.iisc.ac.in/handle/2005/4240

Chicago Manual of Style (16^th Edition):

Rahaman, Md Masiur. “Dynamic Flow Rules in Continuum Visco-plasticity and Damage Models for Poly-crystalline Solids.” 2019. Doctoral Dissertation, Indian Institute of Science. Accessed March 08, 2021. http://etd.iisc.ac.in/handle/2005/4240.

MLA Handbook (7^th Edition):

Rahaman, Md Masiur. “Dynamic Flow Rules in Continuum Visco-plasticity and Damage Models for Poly-crystalline Solids.” 2019. Web. 08 Mar 2021.

Vancouver:

Rahaman MM. Dynamic Flow Rules in Continuum Visco-plasticity and Damage Models for Poly-crystalline Solids. [Internet] [Doctoral dissertation]. Indian Institute of Science; 2019. [cited 2021 Mar 08]. Available from: http://etd.iisc.ac.in/handle/2005/4240.

Council of Science Editors:

Rahaman MM. Dynamic Flow Rules in Continuum Visco-plasticity and Damage Models for Poly-crystalline Solids. [Doctoral Dissertation]. Indian Institute of Science; 2019. Available from: http://etd.iisc.ac.in/handle/2005/4240

Indian Institute of Science

8. Raveendran, Tara. Stochastic Dynamical Systems : New Schemes for Corrections of Linearization Errors and Dynamic Systems Identification.

Degree: PhD, Faculty of Science, 2018, Indian Institute of Science

URL: http://etd.iisc.ac.in/handle/2005/3298

► This thesis essentially deals with the development and numerical explorations of a few improved Monte Carlo filters for nonlinear dynamical systems with a view to… (more)

▼ This thesis essentially deals with the development and numerical explorations of a few improved Monte Carlo filters for nonlinear dynamical systems with a view to estimating the associated states and parameters (i.e. the hidden states appearing in the system or process model) based on the available noisy partial observations. The hidden states are characterized, subject to modelling errors, by the weak solutions of the process model, which is typically in the form of a system of stochastic ordinary differential equations (SDEs). The unknown system parameters, when included as pseudo-states within the process model, are made to evolve as Wiener processes. The observations may also be modelled by a set of measurement SDEs or, when collected at discrete time instants, their temporally discretized maps. The proposed Monte Carlo filters aim at achieving robustness (i.e. insensitivity to variations in the noise parameters) and higher accuracy in the estimates whilst retaining the important feature of applicability to large dimensional nonlinear filtering problems. The thesis begins with a brief review of the literature in Chapter 1. The first development, reported in Chapter 2, is that of a nearly exact, semi-analytical, weak and explicit linearization scheme called Girsanov Corrected Linearization Method (GCLM) for nonlinear mechanical oscillators under additive stochastic excitations. At the heart of the linearization is a temporally localized rejection sampling strategy that, combined with a resampling scheme, enables selecting from and appropriately modifying an ensemble of locally linearized trajectories whilst weakly applying the Girsanov correction (the Radon- Nikodym derivative) for the linearization errors. Through their numeric implementations for a few workhorse nonlinear oscillators, the proposed variants of the scheme are shown to exhibit significantly higher numerical accuracy over a much larger range of the time step size than is possible with the local drift-linearization schemes on their own. The above scheme for linearization correction is exploited and extended in Chapter 3, wherein novel variations within a particle filtering algorithm are proposed to weakly correct for the linearization or integration errors that occur while numerically propagating the process dynamics. Specifically, the correction for linearization, provided by the likelihood or the Radon-Nikodym derivative, is incorporated in two steps. Once the likelihood, an exponential martingale, is split into a product of two factors, correction owing to the first factor is implemented via rejection sampling in the first step. The second factor, being directly computable, is accounted for via two schemes, one employing resampling and the other, a gain-weighted innovation term added to the drift field of the process SDE thereby overcoming excessive sample dispersion by resampling. The proposed strategies, employed as add-ons to existing particle filters, the bootstrap and auxiliary SIR filters in this work, are found to non-trivially improve the… Advisors/Committee Members: Roy, Debasish (advisor), Vasu, Ram Mohan (advisor).

Subjects/Keywords: Stochastic Dynamical Systems; Monte Carlo Filters; Nonlinear Dynamical Systems; Gaussian Sum Filters; Nonlinear Mechanical Oscillators; Nonlinear Dynamic System Identification; Stochatic Nonlinear Oscillators; Dynamic Systems Identification; Girzanov Linearization; Linearization Errors; Stochastic Filters; Stochastic Differential Equations; Nonlinear Dynamic System Identification; Stochastic Filtering; Diffuse Optical Tomography; Girsanov Corrected Linearization Method (GCLM); Applied Physics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Raveendran, T. (2018). Stochastic Dynamical Systems : New Schemes for Corrections of Linearization Errors and Dynamic Systems Identification. (Doctoral Dissertation). Indian Institute of Science. Retrieved from http://etd.iisc.ac.in/handle/2005/3298

Chicago Manual of Style (16^th Edition):

Raveendran, Tara. “Stochastic Dynamical Systems : New Schemes for Corrections of Linearization Errors and Dynamic Systems Identification.” 2018. Doctoral Dissertation, Indian Institute of Science. Accessed March 08, 2021. http://etd.iisc.ac.in/handle/2005/3298.

MLA Handbook (7^th Edition):

Raveendran, Tara. “Stochastic Dynamical Systems : New Schemes for Corrections of Linearization Errors and Dynamic Systems Identification.” 2018. Web. 08 Mar 2021.

Vancouver:

Raveendran T. Stochastic Dynamical Systems : New Schemes for Corrections of Linearization Errors and Dynamic Systems Identification. [Internet] [Doctoral dissertation]. Indian Institute of Science; 2018. [cited 2021 Mar 08]. Available from: http://etd.iisc.ac.in/handle/2005/3298.

Council of Science Editors:

Raveendran T. Stochastic Dynamical Systems : New Schemes for Corrections of Linearization Errors and Dynamic Systems Identification. [Doctoral Dissertation]. Indian Institute of Science; 2018. Available from: http://etd.iisc.ac.in/handle/2005/3298

Indian Institute of Science

9. Gupta, Saurabh. Development Of Deterministic And Stochastic Algorithms For Inverse Problems Of Optical Tomography.

Degree: PhD, Faculty of Engineering, 2017, Indian Institute of Science

URL: http://etd.iisc.ac.in/handle/2005/2608

► Stable and computationally efficient reconstruction methodologies are developed to solve two important medical imaging problems which use near-infrared (NIR) light as the source of interrogation,… (more)

▼ Stable and computationally efficient reconstruction methodologies are developed to solve two important medical imaging problems which use near-infrared (NIR) light as the source of interrogation, namely, diffuse optical tomography (DOT) and one of its variations, ultrasound-modulated optical tomography (UMOT). Since in both these imaging modalities the system matrices are ill-conditioned owing to insufficient and noisy data, the emphasis in this work is to develop robust stochastic filtering algorithms which can handle measurement noise and also account for inaccuracies in forward models through an appropriate assignment of a process noise. However, we start with demonstration of speeding of a Gauss-Newton (GN) algorithm for DOT so that a video-rate reconstruction from data recorded on a CCD camera is rendered feasible. Towards this, a computationally efficient linear iterative scheme is proposed to invert the normal equation of a Gauss-Newton scheme in the context of recovery of absorption coefficient distribution from DOT data, which involved the singular value decomposition (SVD) of the Jacobian matrix appearing in the update equation. This has sufficiently speeded up the inversion that a video rate recovery of time evolving absorption coefficient distribution is demonstrated from experimental data. The SVD-based algorithm has made the number of operations in image reconstruction to be rather than. 2()ONN3()ONN The rest of the algorithms are based on different forms of stochastic filtering wherein we arrive at a mean-square estimate of the parameters through computing their joint probability distributions conditioned on the measurement up to the current instant. Under this, the first algorithm developed uses a Bootstrap particle filter which also uses a quasi-Newton direction within. Since keeping track of the Newton direction necessitates repetitive computation of the Jacobian, for all particle locations and for all time steps, to make the recovery computationally feasible, we devised a faster update of the Jacobian. It is demonstrated, through analytical reasoning and numerical simulations, that the proposed scheme, not only accelerates convergence but also yields substantially reduced sample variance in the estimates vis-à-vis the conventional BS filter. Both accelerated convergence and reduced sample variance in the estimates are demonstrated in DOT optical parameter recovery using simulated and experimental data. In the next demonstration a derivative free variant of the pseudo-dynamic ensemble Kalman filter (PD-EnKF) is developed for DOT wherein the size of the unknown parameter is reduced by representing of the inhomogeneities through simple geometrical shapes. Also the optical parameter fields within the inhomogeneities are approximated via an expansion based on the circular harmonics (CH) (Fourier basis functions). The EnKF is then used to recover the coefficients in the expansion with both simulated and experimentally obtained photon fluence data on phantoms with inhomogeneous inclusions. The… Advisors/Committee Members: Vasu, Ram Mohan (advisor), Roy, Debasish (advisor).

Subjects/Keywords: Optical Tompgraphy; Diffuse Optical Tomography (DOT); Ultrasound Modulated Optical Tomography (UMOT); Inverse Problems; Gauss-Newton Algorithm; Pseuo-Dynamic Ensemble Kalman Filter; Stochastic Algorithms; Stochastic Filtering Algorithms; Medical Imaging; Medical Instrumentation

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Gupta, S. (2017). Development Of Deterministic And Stochastic Algorithms For Inverse Problems Of Optical Tomography. (Doctoral Dissertation). Indian Institute of Science. Retrieved from http://etd.iisc.ac.in/handle/2005/2608

Chicago Manual of Style (16^th Edition):

Gupta, Saurabh. “Development Of Deterministic And Stochastic Algorithms For Inverse Problems Of Optical Tomography.” 2017. Doctoral Dissertation, Indian Institute of Science. Accessed March 08, 2021. http://etd.iisc.ac.in/handle/2005/2608.

MLA Handbook (7^th Edition):

Gupta, Saurabh. “Development Of Deterministic And Stochastic Algorithms For Inverse Problems Of Optical Tomography.” 2017. Web. 08 Mar 2021.

Vancouver:

Gupta S. Development Of Deterministic And Stochastic Algorithms For Inverse Problems Of Optical Tomography. [Internet] [Doctoral dissertation]. Indian Institute of Science; 2017. [cited 2021 Mar 08]. Available from: http://etd.iisc.ac.in/handle/2005/2608.

Council of Science Editors:

Gupta S. Development Of Deterministic And Stochastic Algorithms For Inverse Problems Of Optical Tomography. [Doctoral Dissertation]. Indian Institute of Science; 2017. Available from: http://etd.iisc.ac.in/handle/2005/2608

Indian Institute of Science

10. Saha, Nilanjan. Methods For Forward And Inverse Problems In Nonlinear And Stochastic Structural Dynamics.

Degree: PhD, Faculty of Engineering, 2009, Indian Institute of Science

URL: http://etd.iisc.ac.in/handle/2005/608

► A main thrust of this thesis is to develop and explore linearization-based numeric-analytic integration techniques in the context of stochastically driven nonlinear oscillators of relevance… (more)

▼ A main thrust of this thesis is to develop and explore linearization-based numeric-analytic integration techniques in the context of stochastically driven nonlinear oscillators of relevance in structural dynamics. Unfortunately, unlike the case of deterministic oscillators, available numerical or numeric-analytic integration schemes for stochastically driven oscillators, often modelled through stochastic differential equations (SDE-s), have significantly poorer numerical accuracy. These schemes are generally derived through stochastic Taylor expansions and the limited accuracy results from difficulties in evaluating the multiple stochastic integrals. We propose a few higher-order methods based on the stochastic version of transversal linearization and another method of linearizing the nonlinear drift field based on a Girsanov change of measures. When these schemes are implemented within a Monte Carlo framework for computing the response statistics, one typically needs repeated simulations over a large ensemble. The statistical error due to the finiteness of the ensemble (of size N, say)is of order 1/√N, which implies a rather slow convergence as N→∞. Given the prohibitively large computational cost as N increases, a variance reduction strategy that enables computing accurate response statistics for small N is considered useful. This leads us to propose a weak variance reduction strategy. Finally, we use the explicit derivative-free linearization techniques for state and parameter estimations for structural systems using the extended Kalman filter (EKF). A two-stage version of the EKF (2-EKF) is also proposed so as to account for errors due to linearization and unmodelled dynamics. In Chapter 2, we develop higher order locally transversal linearization (LTL) techniques for strong and weak solutions of stochastically driven nonlinear oscillators. For developing the higher-order methods, we expand the non-linear drift and multiplicative diffusion fields based on backward Euler and Newmark expansions while simultaneously satisfying the original vector field at the forward time instant where we intend to find the discretized solution. Since the non-linear vector fields are conditioned on the solution we wish to determine, the methods are implicit. We also report explicit versions of such linearization schemes via simple modifications. Local error estimates are provided for weak solutions. Weak linearized solutions enable faster computation vis-à-vis their strong counterparts. In Chapter 3, we propose another weak linearization method for non-linear oscillators under stochastic excitations based on Girsanov transformation of measures. Here, the non-linear drift vector is appropriately linearized such that the resulting SDE is analytically solvable. In order to account for the error in replacing of non-linear drift terms, the linearized solutions are multiplied by scalar weighting function. The weighting function is the solution of a scalar SDE(i.e.,Radon-Nikodym derivative). Apart from numerically illustrating the… Advisors/Committee Members: Roy, Debasish (advisor).

Subjects/Keywords: Structural Analysis (Civil Engineering); Stochastic Analysis (Civil engineering); Inverse Problems; Non-linear Oscillations; Stochastically Driven Nonlinear Oscillators; Nonlinear Oscillators - Linearization; Locally Transversal Linearization (LTL); Girsanov Linearization Method; Weak Variance-Reduced Monte Carlo Simulation; Extended Kalman Filter (EKF); Local Linearizations; Stochastic Structural Dynamics; Structural Engineering

Record Details Similar Records Cite « Share

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Saha, N. (2009). Methods For Forward And Inverse Problems In Nonlinear And Stochastic Structural Dynamics. (Doctoral Dissertation). Indian Institute of Science. Retrieved from http://etd.iisc.ac.in/handle/2005/608

Chicago Manual of Style (16^th Edition):

Saha, Nilanjan. “Methods For Forward And Inverse Problems In Nonlinear And Stochastic Structural Dynamics.” 2009. Doctoral Dissertation, Indian Institute of Science. Accessed March 08, 2021. http://etd.iisc.ac.in/handle/2005/608.

MLA Handbook (7^th Edition):

Saha, Nilanjan. “Methods For Forward And Inverse Problems In Nonlinear And Stochastic Structural Dynamics.” 2009. Web. 08 Mar 2021.

Vancouver:

Saha N. Methods For Forward And Inverse Problems In Nonlinear And Stochastic Structural Dynamics. [Internet] [Doctoral dissertation]. Indian Institute of Science; 2009. [cited 2021 Mar 08]. Available from: http://etd.iisc.ac.in/handle/2005/608.

Council of Science Editors:

Saha N. Methods For Forward And Inverse Problems In Nonlinear And Stochastic Structural Dynamics. [Doctoral Dissertation]. Indian Institute of Science; 2009. Available from: http://etd.iisc.ac.in/handle/2005/608

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