• Existence theory for a class of evolutionary equations with time-lag, studied via integral equation formulations

      Baker, Christopher T. H.; Lumb, Patricia M.; University of Chester (University of Chester, 2006)
      In discussions of certain neutral delay differential equations in Hale’s form, the relationship of the original problem with an integrated form (an integral equation) proves to be helpful in considering existence and uniqueness of a solution and sensitivity to initial data. Although the theory is generally based on the assumption that a solution is continuous, natural solutions of neutral delay differential equations of the type considered may be discontinuous. This difficulty is resolved by relating the discontinuous solution to its restrictions on appropriate (half-open) subintervals where they are continuous and can be regarded as solutions of related integral equations. Existence and unicity theories then follow. Furthermore, it is seen that the discontinuous solutions can be regarded as solutions in the sense of Caratheodory (where this concept is adapted from the theory of ordinary differential equations, recast as integral equations).
    • An experimental and computational investigation of pressurised anaerobic digestion

      Wilkinson, Steve; Liang, Zhixuan (University of Chester, 2021-01)
      The aim of this work is to gain a greater understanding of the effect of headspace pressure on biogas production from anaerobic digestion. This is important to improve the energy content of the biogas i.e., increase the methane content and therefore reduce the need for upgrading to scrub out carbon dioxide. In addition, headspace pressure can potentially be used to provide energy for mixing and gas sparging, thereby removing the need for mechanical agitation. In this work, an existing computational model was adapted to investigate its prediction of the variation of biogas production as headspace pressure is increased above atmospheric. The simulation results were accompanied with experimental work using periodic venting of sealed laboratory bottles. The headspace pressure was inferred from the weight loss during venting to atmosphere. In addition, a fully instrumented, pressurised digestor system was designed and constructed in which headspace pressure could be measured directly. Experiments were conducted with headspace pressures of up to 3.4 barg. The biogas that accumulated in the headspace during the digestion process was sampled periodically to determine its composition. The results showed that biogas produced at higher pressures has a higher methane content. A mass balance for the headspace sampling process, which assumed no gas was released from the liquid during sampling, was compared to experimental measurements. This led to the discovery that the effective Henry’s constant for the solubility of carbon dioxide could be an order of magnitude lower in digestate than the known value for pure water. Both the adapted model and the laboratory-scale experiments showed that as the headspace pressure increases, the production rate of biogas decreases. The adapted model also gives slightly higher methane content for higher pressure. The model was then used to estimate the specific growth rates of bacteria used in the laboratory-scale experiments and the agreement was not good, which indicates further changes to the model are needed. The results show that the rate of biogas production reduces as the headspace pressure increases but the rate of decrease is not very steep. This same trend was also displayed for yeast fermentation, which was also studied as another model process for pressurised biological gas production. The variation of the rate of 𝐶𝑂2 evolution with pressure was also used to infer the concentration of dissolved 𝐶𝑂2 within the fermenting yeast cells. Finally, turning attention back to anaerobic digestion processes for energy, it is encouraging that at the relatively modest elevation of pressure required for sparging to give mixing (less than 0.5 barg), the reduction in biogas evolution is small. This small penalty might therefore be offset in a production scale system by the reduced costs of mixing and increased methane content of the biogas.
    • Experimental and process modelling study of integration of a micro-turbine with an amine plant

      Agbonghae, Elvis O.; Best, Thom; Finney, Karen N.; Font Palma, Carolina; Hughes, Kevin J.; Pourkashanian, Mohamed; University of Leeds (Elsevier, 2014-12-31)
      An integrated model of a micro-turbine coupled to a CO2 capture plant has been developed with Aspen Plus, and validated with experimental data obtained from a Turbec T100 microturbine at the PACT facilities in the UKCCS Research Centre, Beighton, UK. Monoethanolamine (MEA) was used as solvent and experimental measurements from the CO2 capture plant have been used to validate the steady-state model developed with Aspen Plus®. The optimum liquid/gas ratio and the lean CO2 loading for 90% CO2 capture has been quantified for flue gases with CO2 concentrations ranging from 3 to 8 mol%.
    • Experimental and theoretical study of a piezoelectric vibration energy harvester under high temperature

      Arroyo, Emmanuelle; Jia, Yu; Du, Sijun; Chen, Shao-Tuan; Seshia, Ashwin A.; University of Cambridge; University of Chester (IEEE, 2017-08-01)
      This paper focuses on studying the effect of increasing the ambient temperature up to 160 °C on the power harvested by an MEMS piezoelectric micro-cantilever manufactured using an aluminum nitride-on-silicon fabrication process. An experimental study shows that the peak output power decreases by 60% to 70% depending on the input acceleration. A theoretical study establishes the relationship of all important parameters with temperature and includes them into a temperature-dependent model. This model shows that around 50% of the power drop can be explained by a decreasing quality factor, and that thermal stresses account for around 30% of this decrease.
    • Experimental demonstration of a transparent graphene millimetre wave absorber with 28% fractional bandwidth at 140 GHz

      Wu, Bian; Tuncer, Hatice M.; Naeem, Majid; Yang, Bin; Cole, Matthew T.; Milne, William I.; Hao, Yang; Queen Mary University of London (Nature Publishing Group, 2014-02-19)
      The development of transparent radio-frequency electronics has been limited, until recently, by the lack of suitable materials. Naturally thin and transparent graphene may lead to disruptive innovations in such applications. Here, we realize optically transparent broadband absorbers operating in the millimetre wave regime achieved by stacking graphene bearing quartz substrates on a ground plate. Broadband absorption is a result of mutually coupled Fabry-Perot resonators represented by each graphene-quartz substrate. An analytical model has been developed to predict the absorption performance and the angular dependence of the absorber. Using a repeated transfer-and-etch process, multilayer graphene was processed to control its surface resistivity. Millimetre wave reflectometer measurements of the stacked graphene-quartz absorbers demonstrated excellent broadband absorption of 90% with a 28% fractional bandwidth from 125-165 GHz. Our data suggests that the absorbers’ operation can also be extended to microwave and low-terahertz bands with negligible loss in performance.
    • Experimental Exploration of CO2 Capture Using a Cryogenic Moving Packed Bed

      Cann, David; Willson, Paul; Font Palma, Carolina; University of Chester; PMW Technology Ltd; University of Chester (SSRN, 2018-10)
      This study examines a novel cryogenic post-combustion capture process, based on a moving bed of cold beads to freeze CO2 out of a flue gas, and this paper presents the first steps in experimental work. The preliminary experiments included the test of fluidization of bed material, if the flow rate of bed material can be kept constant in and out of the column and the estimation of heat transfer coefficient. The obtained results are encouraging for the running of the rig at cryogenic conditions.
    • Experimental exploration of cryogenic CO2 capture utilising a moving bed

      Font-Palma, Carolina; Willson, Paul; Cann, David G. (University of Chester, 2021-04)
      It is widely accepted that climate change is a result of the increase in greenhouse gases in the atmosphere. The continued combustion of fossil fuels and subsequent emission of CO2 is leading to an increase in global temperatures, which has led to interest in decarbonising the energy sector. Carbon capture and storage (CCS) is a method of reducing carbon emissions from fossil fuel power plants by capturing CO2 from exhaust gases and storing it in underground gas stores. Carbon capture using chemical solvents is the most matured technology for capturing emissions from the energy sector, however as the energy sector continues to decarbonise with the arrival of renewable sources focus is shifting to other industries to reduce their carbon footprint. Solvent carbon capture has disadvantages including requiring large equipment and large amounts of heat to regenerate solvent for capture, meaning it would be difficult to scale the technology down and apply it to other industrial applications. Cryogenic carbon capture (CCC) is one proposed method of CCS at smaller scale, which captures CO2 by freezing CO2 out of the exhaust gases as CO2 forms a frost on a heat transfer surface. One disadvantage of CCC is the accumulation of CO2 frost reduces the efficiency of the capture process. The process must be periodically shut down to regenerate the heat transfer surface and collect CO2 that has been frozen out of exhaust gases. This thesis proposes to overcome the frost accumulation through the use of a moving packed bed of small spherical metal beads as the heat transfer surface. As CO2 is fed into a capture column and freezes onto the metal beads, the metal beads are removed from the column, regenerated to recover the CO2, then cooled and recirculated back into the capture column. This prevents the accumulation of frost and allows continuous CO2 capture. There are many difficulties identified in this project, primarily a lack of knowledge on CO2 frost formation and how heat transfer in a moving bed affects frost formation. The research done on a purpose built experimental rig is critical in improving the future design work of a next generation moving bed CCC system. The frost accumulation in a capture column is known as a frost front, which advanced through the capture column at a fixed velocity until the column is saturated with frost. Experimental results had shown that the frost front velocity is predictable for varying CO2 concentrations and gas flow rates, with frost front velocities between 0.46-0.78 mm/s for CO2 concentrations between 4-18% v/v and 0.36-0.98 mm/s for gas flow rates between 50-120 LPM. These frost front velocity experiments in a fixed packed bed allowed the design of a moving packed bed column to set the bed flow rate to match the frost front velocity. The moving bed experiments show that the excessive accumulation of CO2 frost within the capture column can be prevented by utilising the moving bed. The successful development of a moving bed CCC system would result in a cost effective solution to the requirements of certain smaller applications that need to capture CO2, which make up a significant portion of emissions. In particular this technology is very economical for biogas upgrading, where the CO2 content of biogas must be removed before the gas can be introduced to the UK’s larger gas network. There is also a growing interest for use in shipping and other maritime applications, capturing CO2 from ship exhaust emissions during transit.
    • Exploration and Implementation of Augmented Reality for External Beam Radiotherapy

      John, Nigel W.; Vaarkamp, Jaap; Cosentino, Francesco (University of Chester, 2018-07-17)
      We have explored applications of Augmented Reality (AR) for external beam radiotherapy to assist with treatment planning, patient education, and treatment delivery. We created an AR development framework for applications in radiotherapy (RADiotherapy Augmented Reality, RAD-AR) for AR ready consumer electronics such as tablet computers and head mounted devices (HMD). We implemented in RAD-AR three tools to assist radiotherapy practitioners with: treatment plans evaluation, patient pre-treatment information/education, and treatment delivery. We estimated accuracy and precision of the patient setup tool and the underlying self-tracking technology, and fidelity of AR content geometric representation, on the Apple iPad tablet computer and the Microsoft HoloLens HMD. Results showed that the technology could already be applied for detection of large treatment setup errors, and could become applicable to other aspects of treatment delivery subject to technological improvements that can be expected in the near future. We performed user feedback studies of the patient education and the plan evaluation tools. Results indicated an overall positive user evaluation of AR technology compared to conventional tools for the radiotherapy elements implemented. We conclude that AR will become a useful tool in radiotherapy bringing real benefits for both clinicians and patients, contributing to successful treatment outcomes.
    • Exploring the electrochemical performance of graphite and graphene paste electrodes composed of varying lateral flake sizes

      Slate, Anthony J.; Brownson, Dale A. C.; Abo Dena, Ahmed S.; Smith, Graham C.; Whitehead, Kathryn A.; Banks, Craig E. (Royal Society of Chemistry (RSC), 2018)
    • Explosive solutions of a stochastic non-local reaction–diffusion equation arising in shear band formation

      Kavallaris, Nikos I.; University of Chester (Wiley, 2015-07-07)
      In this paper, we consider a non-local stochastic parabolic equation which actually serves as a mathematical model describing the adiabatic shear-banding formation phenomena in strained metals. We first present the derivation of the mathematical model. Then we investigate under which circumstances a finite-time explosion for this non-local SPDE, corresponding to shear-banding formation, occurs. For that purpose some results related to the maximum principle for this non-local SPDE are derived and afterwards the Kaplan's eigenfunction method is employed.
    • Exponential stability in p-th mean of solutions, and of convergent Euler-type solutions, of stochastic delay differential equations

      Baker, Christopher T. H.; Buckwar, Evelyn; Univesity College Chester ; Humboldt-Universität zu Berlin (Elsevier, 2005-12-15)
      This article carries out an analysis which proceeds as follows: showing that an inequality of Halanay type (derivable via comparison theory) can be employed to derive conditions for p-th mean stability of a solution; producing a discrete analogue of the Halanay-type theory, that permits the development of a p-th mean stability analysis of analogous stochastic difference equations. The application of the theoretical results is illustrated by deriving mean-square stability conditions for solutions and numerical solutions of a constant-coefficient linear test equation.
    • Extending an Established Isomorphism between Group Rings and a Subring of the n × n Matrices

      Dougherty, Steven; Gildea, Joe; Korban, Adrian; University of Scranton; University of Chester
      In this work, we extend an established isomorphism between group rings and a subring of the n × n matrices. This extension allows us to construct more complex matrices over the ring R. We present many interesting examples of complex matrices constructed directly from our extension. We also show that some of the matrices used in the literature before can be obtained by a direct application of our extended isomorphism.
    • Fabrication of Graphene Oxide Supercapacitor Devices

      Down, Michael P.; Rowley-Neale, Samuel J.; Smith, Graham C.; Banks, Craig E. (American Chemical Society (ACS), 2018-02-14)
    • Factors for successful Agile collaboration between UX designers and software developers in a complex organisation

      Avis, Nick; Kerins, John; Jones, Alexander J (University of Chester, 2019-07-23)
      User Centred Design (UCD) and Agile Software Development (ASD) processes have been two extremely successful methods for software development in recent years. However, both have been repeatedly described as frequently putting contradictory demands on people working with the respective processes. The current research addresses this point by focussing on the crucial relationship between a User Experience (UX) designer and a software developer. In-depth interviews, an online survey, a contextual inquiry and a diary study are described from a sample of over 100 designers, developers and their stakeholders (managers) in a large media organisation exploring factors for success in Agile development cycles. The findings from the survey show that organisational separation is challenge for agile collaboration between the two roles and while designers and developers have similar levels of (moderately positive) satisfaction with Agile processes, there are differences between the two roles. While developers are happier with the wider teamwork but want more access to and close collaboration with designers, particularly in an environment set up for Agile practices, the designers’ concern was the quality of the wider teamwork. The respondent’s comments also identified that the two roles saw a close – and ideally co-located – cooperation as essential for improving communication, reducing inefficiencies, and avoiding bad products being released. These results reflected the findings from the in-depth interviews with stakeholders. In particular, it was perceived that co-located pairing helped understanding different role-dependent demands and skills, increased efficiency of prototyping and implementing changes, and enabling localised decision-making. However, organisational processes, the setup of work-environment, and managerial traditions meant that this close collaboration and localised decision-making was often not possible to maintain over extended periods. Despite this, the studies conducted between pairs of designers and developers, found that successful collaboration between designers and developers can be found in a complex organisational setting. From the analysis of the empirical studies, six contributing factors emerged that support this. These factors are 1) Close proximity, 2) Early and frequent communication, 3) Shared ideation and problem solving, 4) Crossover of knowledge and skills, 5) Co-creation and prototyping and 6) Making joint decisions. These factors are crucially determined and empowered by the support from the organisational setting and 3 teams where practitioners work. Specifically, by overcoming key challenges to enable integration between UCD and ASD and thus encouraging close collaboration between UX designers and software developers, these challenges are: 1) Organisational structure and team culture, 2) Location and environmental setup and 3) Decision-making. These challenges along with the six factors that enable successful Agile collaboration between designers and developers provide the main contributions of this research. These contributions can be applied within large complex organisations by adopting the suggested ‘Paired Collaboration Manifesto’ to improve the integration between UCD and ASD. Beyond this, more empirical studies can take place, further extending improvements to the collaborative practices between the design and development roles and their surrounding teams.
    • Fibre laser joining of dissimilar materials: Commercially pure Ti and PET hybrid joint for medical device applications

      Chan, Chi-Wai; Smith, Graham C.; Queen's University Belfast; University of Chester (Elsevier, 2016-04-29)
      Laser transmission joining (LTJ) is growing in importance, and has the potential to become a niche technique for the fabrication of hybrid plastic-metal joints for medical device applications. The possibility of directly joining plastics to metals by LTJ has been demonstrated by a number of recent studies. However, a reliable and quantitative method for defining the contact area between the plastic and metal, facilitating calculation of the mechanical shear stress of the hybrid joints, is still lacking. A new method, based on image analysis using ImageJ, is proposed here to quantify the contact area at the joint interface. The effect of discolouration on the mechanical performance of the hybrid joints is also reported for the first time. Biocompatible polyethylene terephthalate (PET) and commercially pure titanium (Ti) were selected as materials for laser joining using a 200 W CW fibre laser system. The effect of laser power, scanning speed and stand-off distance between the nozzle tip and top surface of the plastic were studied and analysed by Taguchi L9 orthogonal array and ANOVA respectively. The surface morphology, structure and elemental composition on the PET and Ti surfaces after shearing/peeling apart were characterized by SEM, EDX, XRD and XPS.
    • Fibre Laser Nitriding of Titanium and its Alloy in Open Atmosphere for Orthopaedic Implant Applications: Investigations on Surface Quality, Microstructure and Tribological Properties

      Chan, Chi-Wai; Lee, Seunghwan; Smith, Graham C.; Donaghy, Clare L.; Queens University Belfast (Chan, Donaghy), Technical University Denmark (Lee), University of Chester (Smith) (Elsevier, 2016-12-20)
      Laser nitriding is known to be an effective method to improve the surface hardness and wear resistance of titanium and its alloys. However, the process requires a gas chamber and this greatly limits the practicability for treating orthopaedic implants which involve complex-shaped parts or curved surfaces, such as the tapered surface in a femoral stemor the ball-shaped surface in a femoral head. To tackle this problem, a direct laser nitriding process in open atmosphere was performed on commercially pure titanium (grade 2, TiG2) and Ti6Al4V alloy (grade 5, TiG5) using a continuous-wave (CW) fibre laser. The effects of varying process parameters, for instance laser power and nitrogen pressure on the surface quality, namely discolouration were quantified using ImageJ analysis. The optimised process parameters to produce the gold-coloured nitride surfaces were also identified: 40W(laser power), 25mm/s (scanning speed), 1.5mm(standoff distance) and 5 bar (N2 pressure). Particularly, N2 pressure at 5 barwas found to be the threshold above which significant discolouration will occur. The surface morphology, composition, microstructure, micro-hardness, and tribological properties, particularly hydrodynamic size distribution of wear debris, were carefully characterized and compared. The experimental results showed that TiG2 and TiG5 reacted differently with the laser radiation at 1.06 μm wavelength in laser nitriding as evidenced by substantial differences in the microstructure, and surface colour and morphology. Furthermore, both friction andwear properties were strongly affected by the hardness and microstructure of titaniumsamples and direct laser nitriding led to substantial improvements in their wear resistant properties. Between the two types of titanium samples, bare TiG2 showed higher friction forces and wear rates, but this trend was reversed after laser nitriding treatments.
    • Fibre laser treatment of beta TNZT titanium alloys for load-bearing implant applications: Effects of surface physical and chemical features on mesenchymal stem cell response and Staphylococcus aureus bacterial attachment

      Donaghy, Clare L.; McFadden, Ryan; Smith, Graham C.; Kelaini, Sophia; Carson, Louise; Malinov, Savko; Margariti, Andriana; Chan, Chi-Wai; Queens University Belfast; University of Chester (MDPI, 2019-03-12)
      A mismatch in bone and implant elastic modulus can lead to aseptic loosening and ultimately implant failure. Selective elemental composition of titanium (Ti) alloys coupled with surface treatment can be used to improve osseointegration and reduce bacterial adhesion. The biocompatibility and antibacterial properties of Ti-35Nb-7Zr-6Ta (TNZT) using fibre laser surface treatment were assessed in this work, due to its excellent material properties (low Young’s modulus and non-toxicity) and the promising attributes of fibre laser treatment (very fast, non-contact, clean and only causes changes in surface without altering the bulk composition/microstructure). The TNZT surfaces in this study were treated in a high speed regime, specifically 100 and 200 mm/s, (or 6 and 12 m/min). Surface roughness and topography (WLI and SEM), chemical composition (SEM-EDX), microstructure (XRD) and chemistry (XPS) were investigated. The biocompatibility of the laser treated surfaces was evaluated using mesenchymal stem cells (MSCs) cultured in vitro at various time points to assess cell attachment (6, 24 and 48 h), proliferation (3, 7 and 14 days) and differentiation (7, 14 and 21 days). Antibacterial performance was also evaluated using Staphylococcus aureus (S. aureus) and Live/Dead staining. Sample groups included untreated base metal (BM), laser treated at 100 mm/s (LT100) and 200 mm/s (LT200). The results demonstrated that laser surface treatment creates a rougher (Ra value of BM is 199 nm, LT100 is 256 nm and LT200 is 232 nm), spiky surface (Rsk > 0 and Rku > 3) with homogenous elemental distribution and decreasing peak-to-peak distance between ripples (0.63 to 0.315 m) as the scanning speed increases (p < 0.05), generating a surface with distinct micron and nano scale features. The improvement in cell spreading, formation of bone-like nodules (only seen on the laser treated samples) and subsequent four-fold reduction in bacterial attachment (p < 0.001) can be attributed to the features created through fibre laser treatment, making it an excellent choice for load bearing implant applications. Last but not least, the presence of TiN in the outermost surface oxide might also account for the improved biocompatibility and antibacterial performances of TNZT.
    • Fibre laser treatment of martensitic NiTi alloys for load-bearing implant applications: Effects of surface chemistry on inhibiting Staphylococcus aureus biofilm formation

      Smith, Graham C.; Chan, Chi-Wai; Carson, Louise; Queens University Belfast; University of Chester (Elsevier, 2018-06-15)
      Biofilm infection is one of the main reasons for implant failure. It is extremely difficult to cure due to its high resistance to antibiotic treatments, and can result in substantial healthcare costs. In this study, the important shape memory NiTi alloy, in its martensitic state, was laser-treated using our newly-developed surface modification technique, aiming to tackle the biofilm infection problem. Martensitic NiTi was chosen for investigation because of its potential advantages in terms of (i) lower elastic modulus and (ii) higher damping capacity over its austenitic counterpart, giving rise to a lower risk of stress shielding and maximum stress between bones and load-bearing implants. The surfaces after laser treatment were systemically analysed using a series of surface measurement (i.e. surface roughness and water contact angle) and material characterisation (i.e. SEM-EDX, XRD and XPS) techniques. The antibacterial performance of the laser-treated surfaces was evaluated using the Staphylococcus aureus (or S. aureus) cells in-vitro cultured at 37 oC for 24h. Fluorescence microscopy accompanied by Live/Dead staining was employed to analyse the cell culture results. The surfaces in their as-received states and after polishing were also tested and compared with the laser-treated surfaces in order to gain a deeper insight in how different surface conditions would influence biofilm formation. Our results indicate that the surfaces after laser treatment can mitigate bacterial attachment and biofilm formation effectively. The antibacterial performance was mainly attributable to the laser-formed oxides which brought desirable changes to the surface chemistry of NiTi. The laser-induced changes in surface roughness and topography, on a micrometre scale, only played a minor role in influencing bacterial attachment. The findings of this study demonstrated for the first time that martensitic NiTi with laser treatment could be a promising choice for the next-generation implants given its superior antimicrobial resistance and favourable mechanical properties for loading bearing applications.
    • Finite Difference Method for Two-Sided Space-Fractional Partial Differential Equations

      Pal, Kamal; Liu, Fang; Yan, Yubin; Roberts, Graham; University of Chester (Springer International Publishing, 2015-06-17)
      Finite difference methods for solving two-sided space-fractional partial differential equations are studied. The space-fractional derivatives are the left-handed and right-handed Riemann-Liouville fractional derivatives which are expressed by using Hadamard finite-part integrals. The Hadamard finite-part integrals are approximated by using piecewise quadratic interpolation polynomials and a numerical approximation scheme of the space-fractional derivative with convergence order O(Δx^(3−α )),10 , where Δt,Δx denote the time and space step sizes, respectively. Numerical examples are presented and compared with the exact analytical solution for its order of convergence.
    • A finite element analysis of impact damage in composite laminates

      Shi, Yu; Soutis, Constantinos; University of Chester; University of Manchester (Cambridge University Press, 2012-12-01)
      In this work, stress-based and fracture mechanics criteria were developed to predict initiation and evolution, respectively, of intra- and inter-laminar cracking developed in composite laminates subjected to low velocity impact. The Soutis shear stress-strain semi-empirical model was used to describe the nonlinear shear behaviour of the composite. The damage model was implemented in the finite element (FE) code (Abaqus/Explicit) by a user-defined material subroutine (VUMAT). Delamination (or inter-laminar cracking) was modelled using interface cohesive elements and the splitting and transverse matrix cracks that appeared within individual plies were also simulated by inserting cohesive elements between neighbouring elements parallel to the fibre direction in each single layer. A good agreement was obtained when compared the numerically predicted results to experimentally obtained curves of impact force and absorbed energy versus time. A non-destructive technique (NDT), penetrant enhanced X-ray radiography, was used to observe the various damage mechanisms induced by impact. It has been shown that the proposed damage model can successfully capture the internal damage pattern and the extent to which it was developed in these carbon fibre/epoxy composite laminates.