The CDSM group specializes in the mechanics of materials and computational analysis. Our primary objective is to comprehend, define, analyze, and enhance the behavior of materials using numerical modeling across a range of time and length scales. Our modeling techniques include molecular dynamics, dislocation dynamics, finite element analysis, data-driven approaches, fuzzy set-based strategies, as well as statistical and stochastic characterization.

Our research encompasses a diverse set of applications, including man-made materials such as elastomer composite materials filled with nanofillers, recycled fiber-reinforced polymer composites, metals, and 3D-printed materials, as well as bio-materials such as bones and teeth. We investigate these materials on different observation scales, ranging from nano- to macro-scale, employing a multi-scale modeling approach to study how these scales interact.

Overall, our research aims to enhance our understanding of material behavior and optimize the use of materials in various applications.

**Current Research Projects**

- Modelling of Recycled Fibre-Reinforced Polymer Composites (Nogol Nazemzadeh, PhD project)
**Aim**: Develop, understand, and predict the behaviour of recycled fibre-reinforced polymers via a comprehensive multi-scale modelling approach.Fiber-reinforced polymer (FRP) composites are engineered materials used in many industries, including aerospace, automobile, sports, and healthcare, due to their excellent strength-to-weight and stiffness-to-weight ratios. Due to their wide usage, these materials, unfortunately, produce industrial scraps and end-of-life parts.

Recycling and reusing composites’ scraps and end-of-life composites could potentially reduce disposal expenses, the demand for new materials and the negative effects on the environment.

Mechanical recycling techniques use grinding techniques to comminute waste materials and create recycled products in smaller size, named flakes (Fig. 1). During the compression molding process, flakes are dropped into the mold randomly. It creates a complicated stochastic meso-structure that makes it difficult to simulate the mechanical behavior. To predict the mechanical properties of recycled composites, large number of test specimens is required, which is time consuming and costly. Therefore, an accurate numerical model to predict the mechanical characteristics of recycled composite will be required.

multiscale modelling brings essential information from material’s lower level of observation to a higher level in order to improve accuracy of material’s behaviour predictions.**Modelling strategy**:Mechanical and geometrical characteristics of fibres, together with properties of a polymer material are taken from the chip-scale to the chip-packing scale. Naturally, the arrangement of flakes on the chip-packing scale affects the overall macroscopic mechanical properties (stiffness and strength).

- Multiscale analysis of polymer composite materials filled with nanofiller using multigrid method (Elizaveta Karaseva, PhD project)
**Aim**: develop a geometry-driven tool for multiscale modelling of composite materials based on elastomers, which would allow predicting the behaviour of new materials without conducting many experiments.Nanofiller reinforced polymer composites in recent years composite materials have been used in almost all areas of industry and science, like transport, aerospace, etc. To manage such material creation and their application, new methods of material analysis techniques and optimisation of well-known are needed. The mechanical material modelling is used for that matter to predict behaviour of the material under load when a full-scale experiment is impossible or requires much experimental repetition.

The polymer composites modelling can be done by the homogenization approach, the principle of which is to replace a heterogeneous medium with homogeneous one with effective properties. Since, the underlying geometry determines the mechanical behaviour of the composite, geometry-driven model is proposed.

In the context of this project, on macroscale, the material is considered a homogeneous structure (scale of observation more than 1 mm). The mesoscale for elastomer-based composite is the observation level, where the polymer matrix considered as a homogeneous material with the filler particles network (scale of observation about 1 mm). The nanofiller forms a network inside the polymer mass made from aggregations and agglomerations. Such a structure can be generated fractally. The microscale is represented by a lower observation level: polymer chains with cross-links, where the polymer chain size is about 0.5 nm width and 200nm long.

This study only considers the mesoscale and macroscale of the material in question. Mesoscale modelling includes modelling the behaviour of these individual elements, followed by modelling the geometry of the structure. Such an engineering problem is reduced to describing the mechanical state of the body using constitutive equations for each material separately. A nanofiller such as Carbon Black is assumed to be a linear elastic material, while elastomer matrix can be described with the strain energy potential of the Ogden model.

The nanofiller forms a network inside the polymer mass made from aggregations and agglomerations. Such a structure can be generated fractally. This generation of a filler network inside a homogeneous elastomer matrix material allows to model the material at the mesoscale. The transition to the macroscale can be done using the multigrid method for homogenization.

The generally accepted approach for describing the deformations of elastomers is using the finite element method.

However, obtaining a practical convergence of the numerical solution by the finite element method when performing a non-linear simulation of a hyperelastic material can be a non-trivial task. Hyperelastic material behaviour analysis requires a mesh to consider the expected deformations of the material. Fine mesh in problems with hyperelastic materials reduces the accuracy of calculations since small finite elements in high deformation zones experience significant shape distortions.

Therefore, the development of new approaches based on mesh resizing can make it possible to solve such problems for hyperelastic materials more efficiently. In recent years, the so-called Multigrid method (MG) has become one of the practical and universal methods for solving systems of equations.

Multigrid method (MG) is the practical method for solving systems of equations to accelerate the convergence of a basic method. In case of MG the iterative process requires significantly fewer computational power to bring the accuracy to the required limits.

- Multi-scale modelling of magneto-elastic materials (Sinan Eraslan, PhD project)
**Aim 1**: understand coupling of magnetism and elasticity, and offer enhanced multi-scale modelling tool that describes material’s behaviour of magneto-elastic composites.**Aim 2**: control and tune the response of magneto-elastic composites by introducing randomness into material’s structure.Smart composite materials have taken a great interest of the researches in the last few decades due to being responsive to external stimulus such as temperature, pH, electric or magnetic field. One particular type of these responsive materials, known as magnetorheological elastomers (MREs), consist of magnetic particles embedded in a silicone based elastomer. These materials present a coupling between magnetism and elasticity via the magnetostriction effect. Magnetostriction is a phenomenon in which a magnetic field leads a change in material shape in ferromagnetic materials. In the MREs, the particles will show magnetostriction when a magnetic field is applied. Thus, some forces will be exerted to the polymer matrix and the composite material will deform. This coupling phenomena proposes various potential applications in many engineering fields, including actuators, sensors, vibration isolation and control, sensing of ultrasonic waves, micro beams/plates in micro-electro-mechanical systems and dialysis membranes in biomedical field. Various magnetic materials such as Terfenol-D, cobalt ferrite, certain earth metals and iron alloys can be used as magnetic filler with several alternatives of elastic matrix such as natural rubber, silicone rubber, vinyl rubber or polyurethane.

The aim of this study is to analyse static and dynamic (e.g. longitudinal wave propagation and stop / pass band formations) behaviour of a magneto-elastic composite material via multiscale modeling approaches. Our goal is to qualify and quantify the influence of magnetic field on material’s response. Our particular interest in this project is the introduction of different degrees of randomness, that gives us the ability to tune and provide the required material’s response (for example – extending the range of filtered-out unwanted wave frequencies).

- Fuzzy logic artificial intelligence approach to mitigation of climate change driven railway track buckling (Iwo Slodczyk, PhD project, UK-NL）
**Aim**: implementation of a fuzzy model which can accurately predict minimum buckling temperatures for given track properties.Buckles in railway track can lead to derailments and result in safety risks and infrastructure repairs. To reduce their occurrence, information about the temperature at which a track has a high risk of buckling is necessary. However, calculating the buckling temperature of track can be a computationally intensive task, which demands precise knowledge of engineering parameters often not available without experimental work.

Fuzzy models allow for computation using uncertain or vague variables, translating linguistic descriptions of properties into a format which allows for calculation and generating a precise, numerical output. In this project, a fuzzy model is developed which can predict buckling temperatures. Here, it is trained using information generated by an analytical track buckling model but it is equally suited to training on field data on real events or a combination of these methods. The model is computationally lightweight and allows for use of uncertain variables based on qualitative assessments of the track. The model is tested against a second set of data, different to the training set, to gauge its predictive capability. A close fit is seen between fuzzy model predictions and the testing set, verifying the functionality of this methodology in the field of railway track buckling.

- Influence of micro-structural properties on wave propagation in heterogeneous media ((Yilang Song, PhD project)
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**Aim 1**: understand and control material characteristics that affect the wave filtering properties of the medium.·

**Aim 2**: employing randomness in a controlled way to influence and optimise the desired material’s behaviour.It is well known that by changing and optimising the microstructure of heterogeneous materials it is possible to control and influence the response of macroscopic media in static as well as dynamic loading conditions. This ability to control and tune the response is particularly important in applications such as waveguide filters, devices that can allow waves at some frequencies to propagate through the material, while at other frequencies waves are stopped. These ranges of frequencies are referred to as pass and stop bands correspondingly. Well described by Brillouin (1946), the phenomenon has mainly been studied in two-phase materials with periodic structure. However, realistic materials are rarely perfectly periodic, thus it is of importance to understand how waveguide technology can be also implemented in more realistic applications.

Analyses of the influence of mechanical and geometrical disorder led to the conclusion that geometrical disorder is significantly more dominant, in comparison to mechanical disorder, affecting the band gap: increasing geometrical randomness leads to the second pass band dropping to zero, i.e. even small perturbations in the geometry make it possible to turn a pass band into a stop band.

Figure 1: The transmission coefficient (y-axis) as a function of frequency (x-axis): randomness added to geometry – the transmission coefficient drops when adding even moderate perturbations to the geometry, eventually transforming an existing (in a periodic material) pass-band into a stop-band.

- Data-driven solutions to 3D-printing dilemma among geometrical design, manufacturing, strength performance and cost-control. (Ruixuan Tu, PhD project)
**Aim 1**(direct): estimate macroscopic characteristics (failure strength) of 3D-printed polylactide components, based on two types of input parameters

- manufacturing variables (e.g. manufacturing angle, infill density, and size of manufacturing voids), and
- geometrical design parameters (e.g. notch root radius).

**Aim 2**(inverse): recommend optimal value of manufacturing variables – infill density, manufacturing angle as well as printing period and material cost, ensuring desired user-defined requirements of design and strength performance.

*Figure 1. (A)Technical drawings of 3D-printed specimens with three different dimensions; (B) Manufacturing angle between the longitudinal axis and the main printing direction**Figure 2. Illustration of using fuzzy inference system for estimation of 3D-printed relevant variables where refers to the direct estimation from manufacturing variables to strength requirement and refers to the inverse estimation which is from given strength and geometrical variables together with cost-relevant ones to locate the optimal combination of manufacturing variables.*Additive manufacturing, often referred to as 3D-printing, has become one of the novel topics in industries, considering its highly customization capability and layer-by-layer deposition characteristic. There are a number of variables which determine the mechanical behaviour (for example a failure strength) of 3D-printed parts, such as infill density, manufacturing orientation, layer thickness, material selection, temperatures etc. The choice of these parameters becomes complicated as the joint effect of them can be hard to predict. Therefore, to avoid being trapped in the complex physics and costly tests, data-driven methodologies can be of great hep, as they learn patterns existing between multiple sets of available data and then uses these patterns to estimate unknown desired parameters.

Data-driven approaches include multiple available techniques such as fuzzy inference system, artificial neural networks, adaptive neural fuzzy inference system etc. They all have different pros and cons, so the method selection depends on the needs of user. In our project, it has been demonstrated, that the failure strength of a 3D-printed part can be estimated with a high accuracy using fuzzy inference system, provided specific manufacturing and geometrical variables. Estimation of the mechanical properties from given parameters (or a set of parameters) of a 3D printer and geometrical specification is an important (first) step in our research; however in order to further solve the industrial dilemma, the optimal value of manufacturing variables – infill density, can also be estimated with user-defined requirements of strength performance and geometrical design.

Moreover, we have also introduced and analysed the effect of printing period and material cost – highly relevant parameters for industries. Thus, we have offered a robust and accurate methodology, which can effectively show the path to the optimal choice on industrial side, as it can not only estimate variables meeting specific requirements but also help controlling the cost of both time and material.

Furthermore, this approach, has a great potential of including other variables which could help industries on the environmental-friendly side. It can be foreseen that the data-driven solution, more specifically the fuzzy inference system, could become a successful decision-making tool when coupled with 5G, real-time data acquisition technologies, big data streams, to model and predict the mechanical behaviour of engineering components and structures.

**Finished Research Projects**

- Numerical Characterisation of Short Fibre Reinforced Composite Materials (Ioannis Ioannou, PhD project)
**Aim**: to investigate the mechanical, thermal and thermo-mechanical overall properties of short fibre-reinforced thermoplastic compositeShort-fibre reinforced composites attract a lot of interest in the industry due to improved performance in various lightweight applications on one hand, and, on the other hand, short-fibre composites are potentially cheaper and easier to produce compared to continuous fibre-reinforced composites.

This project is focused on the analysis and characterisation of microstructurally based mechanical, thermal and thermo-mechanical properties of short fibre thermoplastic reinforced composites (SFRTC) – thermoplastic polymeric matrix reinforced by glass fibre inclusions. As mentioned above, such materials have an advantage to be relatively easily manufactured. Sophisticated shapes of reinforced lightweight structures can be made, when the polymer is introduced into a mould or by hand layup techniques. Once the thermo-mechanical limits of such a composite system are defined, many applications can be covered with many advantages when compared to traditional engineering materials.

This research aims at characterising and generalising the existing knowledge of the mechanical, thermal and thermo-mechanical properties of a SFRTC through a combined numerical and statistical approach. Particular emphasis are put on materials microstructural geometrical properties such as fibres lengths (uniform / non-uniform), aspect ratios, fibres orientations and their influence on the effective proprieties of a composite material.

**Publications**