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  Numerical modelling of cracked engineering materials under dynamic loading

   School of Engineering

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  Dr O Menshykov, Prof I Guz  Applications accepted all year round  Self-Funded PhD Students Only

About the Project

It is common knowledge that all existing structural materials contain various inter- and intra-component cracks and crack-like defects which appear in materials during fabrication or in-service. The presence of structural defects considerably decreases the strength and the reliability of materials.

Under deformation the opposite faces of the existing cracks interact with each other, altering significantly the stress fields near the crack tips. It takes on special significance for the case of high rate deformations as found in impact and high-frequency dynamics, which covers an extremely wide range of situations, where the contact interaction can change the response substantially. Unfortunately, due to the non-linearity of the problem and substantial computational difficulties, even in the simplest case of isotropic homogeneous body, the overwhelming majority of studies neglect the contact interaction of crack faces in spite of its evident significance. In the case of heterogeneous materials, solutions taking the contact interaction into account are non-existent.

This project will start a new direction in fracture mechanics leading to reassessment of the traditional understanding of strength and fracture of cracked materials under dynamic loading. It will be an interdisciplinary work focused on fracture mechanics problems for cracked heterogeneous materials under impact and high-frequency harmonic loading. Special attention will be paid to the effect of the crack faces contact interaction.

The overall aim of the project is the reassessment of dynamic stress intensity factors for cracked materials under dynamic loading taking the crack closure into account.

The main objectives are:

1. Development of a robust numerical methodology for tackling the contact problems, including development of the iterative solution algorithms.

2. Extensive parametric analysis of the problem.

Selection will be made on academic merit. The successful candidate should have (or expect to achieve) a minimum of a UK Honours degree at 2.1 or above (or equivalent) in Engineering, Materials or Applied Mathematics. Fundamentals of Engineering Materials and Stress Analysis, Numerical Methods. The project is likely to involve a combination of analytical studies and computer modelling including FEM&BEM analysis and MatLab programming, so the appropriate computing skills would be quite beneficial but not compulsory.


Formal applications can be completed online:

• Apply for Degree of Doctor of Philosophy in Engineering

• State name of the lead supervisor as the Name of Proposed Supervisor

• State ‘Self-funded’ as Intended Source of Funding

• State the exact project title on the application form

When applying please ensure all required documents are attached:

• All degree certificates and transcripts (Undergraduate AND Postgraduate MSc-officially translated into English where necessary)

• Detailed CV, Personal Statement/Motivation Letter and Intended source of funding

Informal inquiries can be made to Dr O Menshykov ([Email Address Removed]) with a copy of your curriculum vitae and cover letter. All general enquiries should be directed to the Postgraduate Research School ([Email Address Removed])

Engineering (12) Materials Science (24) Mathematics (25)

Funding Notes

This PhD project has no funding attached and is therefore available to students (UK/International) who are able to seek their own funding or sponsorship. Supervisors will not be able to respond to requests to source funding. Details of the cost of study can be found by visiting


1. Menshykova MV, Menshykov OV, Guz IA, Wuensche M, Zhang Ch. A boundary integral equation methods in the frequency domain for cracks under transient loading, Acta Mechanica, 2016, 227(11): 3305-3314.
2. Menshykova MV, Menshykov OV, Guz IA. An iterative BEM for the dynamic analysis of interface crack contact problems, Engineering Analysis with Boundary Elements, 2011, 35: 735-749.
3. Menshykov OV, Menshykova MV, Guz IA. Effect of friction of the crack faces for a linear crack under an oblique harmonic loading, International Journal of Engineering Science, 2008, 46: 438–45