Research
Magnetoelastic models of slender structures
Slender structures abound in many forms in nature, such as trees, leaves, hairs, etc. In engineering, they have numerous applications such as soft continuum robots. However, there is a deficiency in its not being remotely actuated. Incorporation of additional physics such as magnetism in the structures can resolve this limitation. In recent years, slender structures composed of ferromagnetic materials have been used for remote manipulation subjected to weak or moderate external magnetic fields.
It can be resolved by considering structures composed of incorporating an additional physics such as magnetism.
General methodology
We construct the total energy functional consisting of mechanical and micromagnetic energies. The mechanical energy includes elastic strain energy and work due to the external loading device. On the other hand, the micromagnetic energy is composed of exchange, anisotropy, magnetostatic and Zeeman energies. Using tools from variational calculus, we derive the Euler-Lagrange or equilibrium equations.
Mathematical modeling: Obtain total energy functional => Derive governing equations
Total energy = Elastic strain energy + Anisotropic energy + Exchange energy + Demagnetizing energy + Zeeman energy
Numerical simulation :
Using finite difference approach and finite element method to discretize the governing (equilibrium) equations and solve the discretized system of equations subject to the appropriate governing equations
Experimental validation:
Carry out meticulous experiments in the laboratory to validate the numerical results and thereby, the developed mathematical model
Class of slender structures
Magnetoelastic Ribbons:
We have constructed the energy functional for magnetic elastica (we call it MagnetoElastica) by accounting for mechanical energy and various contributing factors of magnetic energy. Using tools from the calculus of variations, we deduce the mathematical model for MagnetoElastica. We proceed to solve the system for various loading scenarios.
Magnetoelastic Rods:
The total magnetoelastic energy functional has been obtained wherein gamma-convergence was used to obtain leading order terms for the magnetic energy. Furthermore, equating the first variational derivative to zero resulted in the Euler-Lagrange or equilibrium equations.
We have put forth our results via a preprint: https://arxiv.org/abs/2401.03447 and a revised manuscript has been submitted to the Journal of Elasticity.
Homogenization of ferromagnetic composites (jointly with Dr. Chinika Dangi, IoE Post Doctoral Fellow, IISc)
Development of mathematical model
We expand the magnetization field over the domain (here, ferromagnetic composite) in terms of an asymptotic series expansion
We utilize two-scale convergence to obtain a generic expression for the total energy functional of ferromagnetic composites
Solution of model configuration
We construct model unit cells with various ordered arrangement of magnetic inclusions and determine the corresponding total energy functional
We solve for magnetization in all configurations and analyze the results
Further validation using finite element simulations
Finite element simulations are setup
Hemodynamics and arterial wall mechanics of Abdominal Aortic Aneurysms
Compared the effect of two geometric indices on the rupture tendency of AAAs
Studied the role of two different constitutive models for blood, namely, Newton and a non-Newtonian Carreau-Yasuda model on hemodynamics
Investigated the influence of St Venant Kirchhoff model and a phenomenological model (developed by Raghavan et al.) on the arterial wall mechanics
More details in the thesis available here.
Proper Orthogonal Decomposition of Unsteady Flow inside Lid Driven Cavity
Flow inside a lid-driven cavity (LDC) is studied here to elucidate bifurcation sequences of the flow at super-critical Reynolds numbers with the help of analyzing the time series at most energetic points in the flow domain. The implication of Recr1 in the context of direct simulation of Navier-Stokes equation is presented here for LDC, with or without explicit excitation inside the LDC.
A detailed enstrophy-based proper orthogonal decomposition (POD) of the flow field is performed to aid in the understanding of the implication of critical Reynolds numbers.
POD of results help us understand the receptivity aspects of the flow field, which give rise to the computed bifurcation sequences. We show that POD modes help one understand the primary and secondary instabilities noted during the bifurcation sequences.
The research has been published in Journal of Mathematical Study and it can be found here.
Multiple Hopf bifurcations in Lid Driven Cavity
Hopf bifurcation phenomenon for singular LDC problem is studied.
Existence of universal critical Reynolds number for primary bifurcation is discussed.
Description of the flow is given, including contour plots and vorticity time series.
A complete database of frequencies involved in this flow is provided.
Sensibility of this problem to numerical experiment conditions is explored.
The research is published in Computer and Fluids and it can be found here.
Linear Dynamics of a Cantilevered Pipe Conveying Fluid
Cantilevered pipe conveying fluid is one of the general class of slender structures with axial flows, e.g. fire-hose and garden-hose
Influence of various system parameters - mass ratio, gravitational parameter, external and internal dissipation - on linear stability of the problem was investigated
More details can be located here.