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Department of Engineering

Current Projects in Mechanics

This page gives descriptions of current projects in the group being tackled by PhD and MScR students, as well as research projects with postdocs. On the lefthand sidebar ther are links to pages covering current research topics in more detail. If anything interests you please contact us


Robust and efficient discontinuous Galerkin topology optimization methods for fluid-solid interactions based on level-set methods (PhD, Thomas Adams)

Optimization plays a very important role in the development of many engineering applications. In this research we are focusing on fluid-solid interactions.
This project aims to develop robust and efficient level-set methods for optimization based on discontinuous Galerkin (DG) methods. We aim to achieve robustness and efficiency using error estimators and adaptivity to control the approximation of the underlying physics and high-order elements to improve the complexity of the methods.


Fracture propagation using discontinuous Galerkin methods (PhD, Robert Bird)

In computational mechanics an accurate and appropriate numerical method for the treatment of crack initiation and propagation is very important in many applications in civil and mechanical engineering. Classical approaches have been shown to render unreliable approximations to the crack propagation path, a fact due to insufficient approximation of the stress field near the crack tip and a crude and inappropriate treatment of the crack growth. When it comes to creating or propagating a fracture, most commercial and customized codes resort to the elimination or removal of the affected elements, which results in a high-mesh dependency of the solution and a completely unphysical behaviour in most cases since the crack ends up following lines given by the mesh in use.
This project aims to address these issues developing new numerical methods based on adaptive discontinuous Galerkin (DG) methods. Moreover, the introduction of adaptivity will improve the accuracy of the approximation of the stress field near the crack tip, making the simulations more reliable.


ExaHyPE - an Exascale Hyperbolic PDE solver Engine (PhD Dominic Charrier, PhD t.b.a.)

ExaHyPE is a new project funded by the European Horizon 2020 initiative. ExaHyPE's mission is to develop a novel simulation engine for hyperbolic PDE problems at exascale. Within the four-year project period, we tackle grand-challenge simulations in Seismology and Astrophysics. Applications include multi-physics earthquake events, exploration scenarios and seismic hazard assessment, as well as the collapse of a binary neutron star system with the anticipated gravitational wave signal. The underlying simulation engine will be based on high-order discontinuous Galerkin discretization on dynamically adaptive Cartesian grids In Durham, we currently started to create ExaHyPE's PDE software infrastructure and to work on communication-/data-reducing patterns for patch-based adaptive Cartesian PDE solvers.


Calculating the Minimum Distance Between Pairs of Triangles on SIMD Hardware for DEM and Unstructured Mesh Contact Point Generation (PhD, Konstantinos Krestenitis)

We study algorithms computing the distances between many rigid bodies represented by triangular meshes. This is an important task for example in discrete element method (DEM) codes. The question is whether we can make this computational geometry challenge scale on all levels of the supercomputer hardware. We know how to obtain excellent vectorisation efficiency, and we have a scaling manycore code. Right at the moment, we thus focus on the efficient distributed memory parallelisation of the contact detection/distance computation.


Dissipation-driven constitutive models for soils (PhD, Rector Mukwiri)

In computational mechanics the yielding of materials has been governed by, so called, yield surfaces that divide stress space into an allowable (elastic) region, inside the yield surface, and an inadmissible region outside the yield surface. Most of these surfaces have been proposed from experimental observations, driven by the need to improve the fit between experimental data and numerical predictions. However, yield surfaces can also be derived from a postulated dissipation function. But, again, current dissipation functions are driven by experimental data rather than a deep understanding of the underlying physics. This project will challenge that convention allowing the constituents of granular materials to dictate the form of the dissipation function.


Peridynamics for dynamic fracture in railway components (PhD, Anira Hashim)

The vast majority of the UK's 32,000km of rail infrastructure is supported by pre-stressed concrete sleepers (PCSs) and crossing bearers (CBs). These concrete members provide lateral restraint and vertical support to the running steel rails. The PCSs and CBs are in turn supported on three sides by track ballast; crushed stone 30-50mm in diameter. Since their introduction in the 1950s, PCSs have superseded traditional wooden sleepers in new track and Network Rail replaces approximately 200,000 timber sleepers each year with PCSs. However, despite the reliance of the UK's rail network on these concrete structures, and the simplicity of their geometry, surprisingly their structural behaviour is poorly understood. There are concerns that the development of fractures in concrete supporting members is undermining the rail network. In order to maintain a safe, reliable and resilient rail network it is essential to understand how the concrete support systems can be designed to future proof them against ever increasing structural demands.

The majority of engineering numerical analyses use the mesh-based finite-element method (FEM). However, the FEM suffers from a number of drawbacks when trying to model fracture propagation. Its main limitation lies in the direct coupling of the material deformation with the mesh used to integrate the problem domain. A consequence of this is the computationally cumbersome task of re-meshing and transferring of internal variables associated with material deformation as the crack front advances. An alternative is to use an enrichment method to represent discontinuities; however these methods suffer from numerical stability issues. The research proposed here will use an alternative mesh-free method; peridyanamics.

A key part of the project will be the implementation of a 3D peridynamics research code that allows for fracture propagation in concrete materials. This code will then be used to analyse the structural behaviour of PCSs and CBs under dynamic traffic loads.


Implicit material point methods for geotechnical analysis (PhD, Tim Charlton)

The Material Point Method (MPM) is a numerical analysis technique that allows solid mechanics problems with large deformation and non-linearity to be modelled (an area where conventional mesh-based approached often struggle) using particles at which state variables are stored and tracked. Calculations are then carried out on a regular background grid to which state variables are mapped from the particles. The general focus of this work is implementing the MPM using an implicit scheme (the majority of previous work has used an explicit implementation), extending this and applying to non-linear finite deformation problems. A problem in the original MPM method is that non-physical jumps in stresses arise when a material point crosses the boundary between one background grid cell and another. This problem is addressed by the Generalised Interpolation Material Point (GIMP) method. The GIMP method attempts to alleviate this problem by modifying the particle characteristic function so that particles have an influence on nodes other than those associated with the element it is inside. This research will develop an implicit implementation of the GIMP method, including geometric and material non-linearities that are essential to model problems in geotechnical engineering.


Boundary approximations in the Material Point Method (MScR, Yun Bing)

The vast majority of boundary value numerical analyses in engineering are conducted using the finite-element method (FEM). However, the conventional FEM suffers from a number of drawbacks, principally its inability to handle large deformations and fracture without the computationally expensive task of re-meshing. This makes the simulation of such problems numerically tiresome. An alternative to the FEM that overcomes some of these issues is the material point method (MPM). The MPM is similar to the FEM in that it splits a problem domain into a number of smaller cells (or elements) and solves the physical equations at discrete points on this “mesh”. The main advantage of MPM over FEM is in its ability to easily handle large deformations and therefore has significant potential in areas where the FEM currently struggles

However, in the finite-element method, boundaries of the problem domain coincide with element boundaries. However, if we instead discretize a problem domain with discrete points (or nodes) rather than a mesh we no longer have a clear interpretation of the boundary of our domain. The current literature on the MPM fails to address (or even mention) this problem. This research project proposes to develop new ways to model and track a boundary in a solid mechanics problem where there are finite deformations.


Resilient rail infrastructure: dissipation driven fracture analysis of concrete support systems (PDRA, TBC)

The vast majority of the UK's 32,000km of rail infrastructure is supported by pre-stressed concrete sleepers (PCSs) and crossing bearers (CBs). These concrete members provide lateral restraint and vertical support to the running steel rails. The PCSs and CBs are in turn supported on three sides by track ballast; crushed stone 30-50mm in diameter. Since their introduction in the 1950s, PCSs have superseded traditional wooden sleepers in new track and Network Rail replaces approximately 200,000 timber sleepers each year with PCSs. However, despite the reliance of the UK's rail network on these concrete structures, and the simplicity of their geometry, surprisingly their structural behaviour is poorly understood. In order to maintain a safe, reliable and resilient rail network it is essential to understand how the concrete support systems can be designed to future proof them against ever increasing structural demands.

This two-year research project is concerned with three-dimensional dynamic analysis to assess the structural robustness of PCSs and CBs using a novel computational mechanics framework and associated numerical analysis technique. If successful, this research will provide a transformative, complete and consistent framework for modelling fracture in a variety of engineering materials. The creativity of this proposal lies in the application of up-to-the-minute ideas in constitutive modelling, fracture mechanics and numerical analysis techniques to a poorly understood yet critical component of the UK's rail infrastructure. It will provide a framework within which to develop new resilient rail-support system fastening methods.

More details here.


iSmart (Infrastructure slopes: Sustainable Management And Resilience Assessment) (PDRA: JD Asquith)

The UK's transport infrastructure is one of the most heavily used in the world. The performance of the road and rail networks is critically dependent on the performance of the cutting and embankment slopes that make up £20 bn of the £60 bn asset value of major highway infrastructure alone. Many of these slopes are old and suffer high incidents of instability, which are increasing with time. This project to investigate the impacts of climate changes on these slopes is funded by the Engineering and Physical Sciences Research Council (EPSRC) and forms a unique opportunity uniting six academic institutions (Durham, Newcastle, Southampton, Queens Belfast, Loughborough Universities and British Geological Survey) and combining their field, laboratory and computing facilities. The work at Durham University is to undertake triaxial testing of embankment fill materials in unsaturated conditions to investgate the changes induced by cycles of wetting and drying. The unsaturated soil laboratory at Durham Unversity is also determining soil water retention curves to investigate water retention and volume changes of the soil during dring and wetting.

For more details see ismartproject.org.


Development and use of meshless point collocation methods (PhD, Lei Fan)

The design and implementation of high efficiency meshless methods are attractive goals for the numerical solution of engineering problems modelled using partial differential equations. The weak form-based meshless methods face several challenges such as the complexity of integration and implementation of boundary conditions. A strong form meshless point collocation method based on a reproducing kernel particle approximation is to be developed in this project alongside theoretical development and numerical implementation. It is considered as a truly meshless method since no background mesh and no integration are required. Applying this meshless point collocation method to fracture modelling and geometrically non-linear elastic problems remains a challenging topic in computational solid mechanics. This project comprises two major parts: firstly an investigation into the theory of strong form collocation methods, and secondly an innovative numerical framework for fracture and geometrically non-linear elastic modelling using this meshless point collocation method based on the reproducing kernel particle method.


Meshless method for fracture modelling: a new cracking particle method (PhD, Weilong Ai)

Conventional numerical methods meet dilemmas when applied for fracture modelling. In the Finite Element Method (FEM), a crack is forced to propagate along mesh edges so the accuracy of results depends on the quality of meshes. The relevance to meshes is relieved in meshless methods, in which the problem domain is discretised by nodes alone. So problems in the FEM, including mesh distortion and volumetric locking, can be avoided. The level set method has been associated with meshless methods for fracture simulation, but the expense of updating level set functions is not cheap. An alternative is through the Cracking Particle Method (CPM), which describes crack paths by the use of a set of particles with discontinuous segments, and the updating of cracks is simple by adding or deleting cracking particles rather than those by updating level set functions. However, there are some limitations of the CPM: one is that a large number of nodes are required to obtain accurate results; for another the CPM suffers from spurious crack propagation. This project is aimed to solve the two main problems mentioned above. New strategies of cracking particles will be proposed to improve the accuracy and an adaptivity approach will be introduced to control the number of nodes. Finally a robust method will be developed which can provide accurate results but maintain the calculating efficiency.


Modelling of Seabed Ploughing using the Material Point Method (PDRA, Michael Cortis)

Soil ploughing, an activity carried out by humankind for thousands of years is now being used at a larger scale to form seabed trenches, and lay cables and pipeline to connect offshore energy production and generation devices to the supply network. In the next 50 years many more of these offshore devices (wind, wave, current and oil & gas) will be installed, meaning that considerably more seabed ploughing will be undertaken. However, we do not possess the same level of understanding of the mechanical and hydraulic processes associated with soil ploughing as we have developed for other soil-structure interaction problems. This means that ploughing schemes and equipment have to be designed on the basis of semi-empirical and conservative approaches, leading to financial uncertainty. In this project, the Material Point Method will be used to simulate seabed ploughing and provide better estimates of key parameters such as the towing force and speed of ploughing in a given seabed deposit, along with insights into plough stability. This will be achieved by the development of a robust 2D/3D MPM software able to model large geotechnical problems that can lead to major savings in the offshore cable and pipeline installation industry.


Numerical modelling of screw pile installation for wind energy foundation systems (PDRA Dr Lei Wang)

An EPSRC-funded project where, at Durham we are developing the Material Point Method as a tool for prediction of the behaviour of screwpile foundations. The project website is here.