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Multiscale modelling and multifield analysis of composite structures

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  • Full or part time
    Dr F Fazzolari
  • Application Deadline
    No more applications being accepted
  • Funded PhD Project (European/UK Students Only)
    Funded PhD Project (European/UK Students Only)

Project Description

Nanosciece and nanocomposites gave birth to a new era in material science, engineering, medicine, electronics, energy harvesting/production. The capability to manipulate materials at atomic and molecular level has created structures with unique functionalities and characteristics.

In this context, revolutionary has been the creation of new advanced materials such as carbon nanotube (CNT) composites [1]. They possess extraordinary mechanical, thermal and electrical properties with providing strong, light and high toughness characteristics. These astonishing properties make them the ideal candidate for the reinforcement of polymeric materials. The key point is to transfer their properties to the polymeric matrix system. In this respect, two main issues have to be solved to effectively improve the material properties of CNTs reinforced composites. These are the interfacial adhesion between the reinforcements and the polymer and their dispersion in the polymer matrix system.

However, when it comes to the structural analysis of nanocomposites, generally experts rely either on experiments, which are very expensive at the nanoscale, or on three main approaches directly related to the computational modelling [2]: (i) atomistic modelling; (ii) hybrid atomistic-continuum mechanics; (iii) continuum mechanics. The atomistic modelling encompasses computational techniques such as molecular dynamics (MD), tight-binding molecular dynamics (TBMD) and density functional theory (DFT). They usually lead to high accurate results but at a prohibitive computational cost. A similar drawback affects the hybrid atomistic-continuum mechanics modelling. Pure continuum mechanics is significantly less expensive than the other two and the theoretical formulations are relatively simple. However, despite these advantages, the continuum mechanics approach is featured by a fundamental flaw, which consists in considering the CNTs as continuous and homogeneous macrostructures while in contrast their material microstructures, made up of lattice spacing between individual carbon atoms covalently bonded, is completely discarded. Although many efforts have been put in place concerning the use of classical continuum mechanics at small scale, their employment is not completely reliable. The limited applicability is due to the fact that at small size the lattice spacing between individual atoms becomes increasingly important and the discrete structure of the material can no longer be homogenized into a continuum. More specifically, the material properties at the nano-scale are size dependent and thus the small length scale effects should be considered for a better prediction of the mechanical behaviour of nano-materials. As a result of that, various researchers [3] suggested caution while applying the classical continuum mechanics models to nanomaterials. For all these reasons, the latest research on this topic is focused on the development of ad-hoc continuum mechanics models able to take into account the size dependence in nanomaterials. This research area is referred to as nonlocal continuum mechanics [4].

The main purpose of this project is to derive a generalised nonlocal elasticity theory capable to accurately analyse the newest nanocomposites used in real life applications. The new formulation based on advanced structural models [5, 6, 7], will also take into account coupled multi-field (mechanical, thermal, electrical and magnetic) effects. To this aim, the project will be split into two main objectives:

• the theoretical development of a new formulation for modelling small-scale effects in nanomaterials and nanostructures accounting for multiphysical/multifield effects.

• the computational implementation of the new formulation in a software able to support effectively the design process of a significant number of nanomaterials and nano-structures, for electronic, medical, bio-mechanical, mechanical and aerospace applications.

Funding Notes

The studentship will be funded by EPSRC DTA, covering tuition fees at the UK/EU rate for 3.5 years of your PhD and an annual stipend for 3.5 years of £15,009 per annum. To be eligible for this funding the candidate should be a UK citizen or an EU citizen that meets the EPSRC’s eligibility criteria


[1] Iijim S., Helical microtubules of graphitic carbon, Nature, 354, 56-58, 1993.
[2] Arash B., Wang Q. A review on the application of nonlocal elastic models in modeling of carbon
nanotubes and graphenes, Computational Material Science, 51, 303-313, 2012.
[3] Peddieson J., Buchanan R. G., McNitt R. P., Application of nonlocal continuum models to
nanotechnology, International Journal of Engineering Science, 41, 305-312, 1976.
[4] Eringen A. C., Nonlocal Continuum Field Theories, First Edition, Springer, 2002, NewYork.
[5] Fazzolari, F. A. (2018). Generalized exponential, polynomial and trigonometric theories for
vibration and stability analysis of porous FG sandwich beams resting on elastic foundations.
Composites Part B: Engineering, 136, 254-271. doi:10.1016/j.compositesb.2017.10.022
[6] Fazzolari, F. A. (2016). Quasi-3D beam models for the computation of eigenfrequencies of
functionally graded beams with arbitrary boundary conditions. Composite Structures, 154, 239-
255. doi:10.1016/j.compstruct.2016.06.042
[7] Fazzolari, F. A. (2018). Thermoelastic vibration and stability of temperature-dependent carbon
nanotube-reinforced composite plates. Composite Structures, 196, 199-214.

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