The document outlines the research interests of Professor Sondipon Adhikari in the mechanics of materials and structures, focusing on hollow structures and their advantages for sustainable engineering. It discusses key principles such as equivalent elastic properties, wave propagation analysis, buckling of lattice materials, and elastic tailoring of materials for enhanced performance. The document also references several research works and employs both analytical and machine learning approaches to investigate the behavior of these structures.

1. A hollow future for engineering structures:
Design and analysis principles
Sondipon Adhikari
Professor of Engineering Mechanics
James Watt School of Engineering

2. 2
My research interests
Mechanics of materials
and structures across
length-scales
 Mechanics of metamaterials
 Dynamics of nonlocal continuous
systems
 Atomistic computational method -
Finite element / Molecular
mechanics
 Structural dynamics using
continuum theory
 Cellular materials and honeycomb
structures
 Wave propagation, buckling and
mechanical analysis
 Shape optimisation and design
Digital twins and inverse
problems
 Nanomechanical sensors
 Identification of nonlinear systems
 Model updating and damage detection
 Identification of damping
 Digital twins
Dynamics of complex
systems
 Discrete damped systems
 Continuous systems
 Nonviscously damped discrete systems
 Nonlocal damped continuous systems
Vibration energy harvesting
/ wind energy
 Nonlinear vibration energy harvesting
 Energy harvesting under uncertainty
 Dynamics of wind turbines
Uncertainty quantification in
computational mechanics
 Dynamics of stochastic systems
 Random eigenvalue problem
 Random matrix theory for structural dynamics
 Computational methods for uncertainty
propagation

3. Hollow structures
• Hollow structures are present in both
human made systems and natural
systems across different length
scales.
• They are lightweight and uses less
materials compared to their “solid”
counterparts.
• Hollow structures have the potential
for sustainable developments in civil,
mechanical and aerospace
engineering
• Understanding their mechanical and
dynamic behavior is important to
employ them in engineering
structures.

4. Equivalent elastic properties
• There are five elastic properties which
quantify equivalent elastic properties
of 2D lattices
[1] Muherkee, S. and Adhikari, S., "The
in-plane mechanics of a family of
curved 2D lattices", Composite
Structures, 280[1] (2022), pp. 114859.
[2] Adhikari, S.,, Mukhopadhyay, T.,
and Liu, X., "Broadband dynamic
elastic moduli of honeycomb lattice
materials: A generalized analytical
approach", Mechanics of Materials,
157[6] (2021), pp. 103796.
[3] Muherkee, S. and Adhikari, S., "A
general analytical framework for the
mechanics of heterogeneous
hexagonal lattices", Thin-Walled
Structures, 167[10] (2021), pp. 108188.
[4] Mukhopadhyay, T. Adhikari, S. and
Alu, A., "Theoretical limits for negative
elastic moduli in sub-acoustic lattice
materials", Physical Review B, 99[9]
(2019), pp. 094108.
[5] Mukhopadhyay, T., Adhikari, S. and
Batou, A., "Frequency domain
homogenization for the viscoelastic
properties of spatially correlated quasi-
periodic lattices", International Journal
of Mechanical Sciences, 150[1] (2019),
pp. 784-806.
• A “bottom-up” approach is adopted,
where a mechanical analysis is
performed on a unit cell. The unit cell
tessellates and covers the 2D space.

5. O A B C O
0
2
4
6
8
10
12
14
16
18
20
Wave propagation analysis
• For lattices with perfectly periodic
units, Bloch wave analysis is
performed using periodic boundary
conditions
• When there are lattice structures
with micro‐structural variabilities, a
machine learning based
computational approach is
developed.
[1] Chatterjee, T., Karlicic, D., Adhikari,
S. and Friswel, M. I., "Wave
propagation in randomly parameterized
2D lattices via machine learning",
Composite Structures, 275[11] (2021),
pp. 114386.
[2] Cajic, M., Karlicic, D., Paunovic, S.
and Adhikari, S., "Bloch waves in an
array of elastically connected periodic
slender structures", Mechanical
Systems and Signal Processing, 155[6]
(2021), pp. 107591.
[3] Karlicic, D., Cajic, M., Chatterjee, T.
and Adhikari, S., "Wave propagation in
mass embedded and pre-stressed
hexagonal lattices", Composite
Structures, 256[1] (2021), pp. 113087.
[4] Adhikari, S., Mukhopadhyay, T.,
Shaw, A. and Lavery, N. P., "Apparent
negative values of Young's moduli of
lattice materials under dynamic
conditions", International Journal of
Engineering Science, 150[5] (2020), pp.
103231.
[5] Mukhopadhyay, T. Adhikari, S. and
Alu, A., "Theoretical limits for negative
elastic moduli in sub-acoustic lattice
materials", Physical Review B, 99[9]
(2019), pp. 094108.

6. Buckling of lattice materials
• Elastic instability such
as the buckling of
cellular materials plays
a pivotal role in their
analysis and design.
• Despite extensive
research, the
quantification of critical
stresses leading to
elastic instabilities
remains challenging
due to the inherent
nonlinearities.
• We develop an
analytical approach
considering the
spectral
decomposition of the
elasticity matrix of two-
dimensional
hexagonal lattice
materials.
[1] Adhikari, S., "The in-plane
mechanical properties of highly
compressible and stretchable 2D
lattices", Composite Structures, 9[6]
(2021), pp. 589.
[2] Adhikari, S., "Exact transcendental
stiffness matrices of general beam-
columns embedded in elastic
mediums", Computers and Structures,
255[10] (2021), pp. 106617.
[3] Adhikari, S., "The eigenbuckling
analysis of hexagonal lattices:
Closed-form solutions",
Proceedings of the Royal Society of
London, Series - A, 477[2251] (2021),
pp. 20210244.
[4] Larsen, M. K., Adhikari, S. and
Arora, V., "Analysis of stochastically
parameterised prestressed beams and
frames", Engineering
Structures, 249[12] (2021), pp. 113312.

7. Elastic tailoring of lattice materials
 Miniplate bulk properties through optimal micro-
structure designs through material selection and
external stimulation
 Piezo-electric materials: voltage application
 Magnetostrictive materials: magnetic field application
 Multimaterial lattice composition: stress field application
7
[1] Singh, A., Mukhopadhyay,
T., Adhikari, S. and Bhattacharya, B.,
"Active multi-physical modulation of
Poisson's ratios in composite
piezoelectric lattices: On-demand sign
reversal", Composite Structures, 280[1]
(2022), pp. 114857.
[2] Singh, A., Mukhopadhyay, T.,
Adhikari, S. and Bhattacharya, B.,
"Voltage-dependent modulation of
elastic moduli in lattice metamaterials:
Emergence of a programmable state-
transition capability", International
Journal of Solids and Structures, 208-
209[1] (2021), pp. 31-48.
[3] Chatterjee, T., Chakraborty, S.,
Goswami, S., Adhikari, S. and Friswell,
M. I., "Robust topological designs for
extreme metamaterial micro-
structures", Nature Scientific Reports,
11[7] (2021), pp. 15221.
[4] Mukhopadhyay, T., Naskar, S. and
Adhikari, S., "Anisotropy tailoring in
geometrically isotropic multi-material
lattices", Extreme Mechanics Letters,
40[10] (2020), pp. 100934.
 Optimal micro-structure designs
such that macroscopic properties
of anisotropic lattices follow
specific prescribed designer
values.
 It will result in novel micro-
architectured lattices with extreme
Poisson's ratio and elastic moduli.

8. @ ProfAdhikari
Sondipon Adhikari (Infrastructure & Environment)
James Watt School of Engineering
Room no 643, James Watt South Building
The University of Glasgow
Phone: + 44 (0) 141 330 3317
Email: Sondipon.Adhikari@glasgow.ac.uk
http://www.gla.ac.uk/schools/engineering/staff/sondiponadhikari
Google Scholar page:
http://scholar.google.co.uk/citations?user=tKM35S0AAAAJ