Simulating large deformation processes using an explicit element-free Galerkin method
: With applications to material forming

  • Stephen Smith

Student thesis: Doctoral ThesisDoctor of Philosophy


Computational methods are widely utilised in engineering to obtain the response of components and structures under loading. In the pioneering years, modest computational power limited the application of these computational techniques to relatively simple problems. However, with the substantial increase in computational power, the scope of these methods has broadened to simulate several physical processes used in industry to inform manufacturing strategies.

A forming technique that has benefited from this increased computational power is the stretch blow moulding (SBM) process, which is the primary manufacturing technique used to produce polymer bottles for the water and soft drinks industry. The finite element method is frequently used to simulate this process, to reduce the economic cost of bottle design and optimise for minimum material use. Despite its ubiquitous adoption, several issues are often encountered in finite element simulations, predominately related to the dependency of the results on the set of elements (mesh) used to solve the problem. In response to these issues, so-called meshfree methods have been developed. Despite twenty years of progress in meshfree technology, the application of these techniques to real-world applications is limited. This thesis aims to further widen the application of meshfree methods to material-forming, where the absence of a fixed computational mesh has the potential to provide numerous benefits.

In this work, an explicit element-free Galerkin method was used to simulate a range of large deformation problems. Initially, a total formulation was utilised, in which the neighbourhood information was kept constant throughout. Through several numerical examples, the benefits of meshfree methods in the simulation of large deformation problems were shown. The application of this total formulation culminated in a validated simulation of the stretch blow moulding process.

In the final part of this work, the formulation was enhanced to include updates of the neighbourhood information. This development includes a novel method to implement an evolving domain of influence into the general shape function scheme. This new formulation was validated through several examples, with the potential benefits of the approach outlined.
Date of AwardJul 2020
Original languageEnglish
Awarding Institution
  • Queen's University Belfast
SponsorsNorthern Ireland Department for the Economy
SupervisorBrian Falzon (Supervisor) & Gary Menary (Supervisor)


  • Computational mechanics
  • Meshfree methods
  • Material forming

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