Research

Magnetoelastic models of slender structures (with Prof. Vivekanand Dabade, Asstt. Professor, Department of Aerospace Engineering, IISc)

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 methodology: We use continuation methods to obtain the nonlinear deformation of the ferromagnetic structures capturing primary and secondary bifurcations, namely, pitchfork, folds. We also used Auto-07p, an advanced mathematical tool to verify our results. For ascertaining stability of the deformed configurations, we employ a Sturm-Liouville formulation of the second variation of the energy functional.
Experimental validation:

Carry out meticulous experiments in the laboratory to validate the numerical results and thereby, the validity of 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.

Publications

G. R. K. C. Avatar and V. Dabade, “Kirchhoff’s analogy for a planar deformable ferromagnetic rod,” Journal of Applied Mechanics. ASME International, pp. 1–12, Mar. 20, 2025. DOI: 10.1115/1.4068252.
G. R. Krishna Chand Avatar and Vivekanand Dabade, “Deformation of a planar ferromagnetic elastic ribbon,” Journal of Elasticity, vol. 157, no. 1, Dec. 10, 2024. DOI: 10.1007/s10659-024-10100-w.

Homogenization of ferromagnetic composites (with Dr. Chinika Dangi, IoE Post Doctoral Fellow, IISc (currently Asst Prof, Amrita Vishwa Vidyapeetham)

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

Domain Reduction Method in Geomechanics (led by Bhavesh Banjare)

Stochastic analysis of 3D tunnels in near-fault ground motion (Link)

Stochastic tunnel response analysis: Monte Carlo simulations with 3D soil–tunnel–fault models (via MASTODON) evaluate how uncertainties in shear wave velocity and soil type (soft, medium, hard) influence tunnel behavior under near‑fault earthquakes.
Efficient large‑scale modeling: The Domain Reduction Method reduces computational cost while revealing that tunnel dynamics are highly sensitive to local site effects, ground motion characteristics, and rock stiffness.

Three-Dimensional Seismic Response Analysis of Tunnels in Layered Media using Modified Domain Reduction Method (Link)

MDRM for tunnel–fault systems: A multi‑layer Modified Domain Reduction Method (MDRM), implemented in MASTODON, efficiently models Soil–Fault–Tunnel interactions in layered soils, capturing seismic source, wave propagation, and local site effects.
Key findings: Parametric studies across fault rupture types and tunnel cross‑sections show that fault inclination, surface wave generation, and soil layering strongly influence tunnel seismic response, guiding safer underground design.

Variational formulation of domain reduction method (ongoing)

Under process

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.

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