Research theme two of five
Mechanics of materials, metamaterials and architected systems
Metamaterial theory assumes perfect periodicity. Every fabricated sample violates it. This theme is about what disorder does to the properties that make architected materials useful.
The problem
Additive manufacturing leaves geometric scatter of a few per cent in strut thickness and node position, and material properties vary between batches. The gap between predicted and measured attenuation in published experiments is frequently attributed to this and rarely quantified.
The question is what randomness does to the objects that make metamaterials useful. Band gaps widen, narrow or fragment. Attenuation acquires a distribution. Localisation appears in structures designed to transmit. Topological interface states are claimed to be protected against disorder, and the strength of that protection is a quantitative question still open for elastic systems.
Why it matters
A band gap computed at nominal geometry is the best case a lattice will ever see. Manufactured cells carry tolerance, and the gap edges smear across the population, so the attenuation a customer measures sits somewhere in a distribution whose width the nominal calculation says nothing about. A specification needs the whole distribution: the attenuation that holds across the tolerance band, and what nominal performance it costs to get there. This is what decides whether an architected panel can be specified for vibration attenuation in an aircraft, a vehicle or a defence structure, and it is where additive manufacturing binds hardest, since tolerance is the constraint that scales worst as cells get smaller.
Current frontier
- disordered and stochastic metamaterials
- periodic and quasiperiodic lattices
- band-gap statistics under manufacturing tolerance
- topological interface states and the limits of protection
- inertial amplification and beyond-nearest-neighbour coupling
- dynamic homogenisation and effective moduli
- curved-beam and hierarchical lattices
- inverse and generative design of architected materials
Signature concepts
- band-gap statistics
- localisation
- dynamic effective properties
- metadamping
- non-reciprocity
Open problems
- Given a distribution on unit-cell geometry, what is the distribution of the band-gap edges?
- At what disorder strength does an engineered interface state stop being protected?
- Can a lattice be designed so that its attenuation holds up across the whole manufacturing tolerance, and how much nominal performance does that cost?
Selected papers
- Enhancement of band-gap characteristics in hexagonal and re-entrant lattices via curved beams
S. Mukherjee, M. Cajić, D. Karličić, S. Adhikari · Composite Structures 306, 116591 · 2023 - Non-reciprocal wave propagation in time-modulated elastic lattices with inerters
D. Karličić et al. · Applied Mathematical Modelling 117, 316-335 · 2023 - Tailoring band gap properties of curved hexagonal lattices with nodal cantilevers
S. Mukherjee et al. · Composite Structures 345, 118342 · 2024 - Metaharvesting: emergent energy harvesting by piezoelectric metamaterials
I. Patrick, S. Adhikari, M. I. Hussein · Proceedings A 480(2301), 20240033 · 2024 - Meta-dissipation: quantifying energy dissipation in dissipative discrete periodic metamaterials
A. Banerjee, K. K. Bera, S. Adhikari · Applied Physics Letters 127(12) · 2025 - Effective elastic mechanical properties of single layer graphene sheets
F. Scarpa, S. Adhikari, A. Srikantha Phani · Nanotechnology 20, 065709 · 2009
Foundations
Cellular and lattice materials, composites, multiscale mechanics, and the nanoscale and nonlocal work on graphene, boron nitride, carbon nanotubes and nonlocal beam theory. The line runs from nanostructures through multiscale mechanics and cellular materials to architected and then disordered metamaterials.