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Research interests

I work in the area of applied analysis, studying variational problems and partial differential equations that arise in continuum mechanics, in particular in nonlinear elasticity. A common feature of the problems studied is the often intriguing interplay between the properties of the underlying partial differential equations and the physics of the situation being modelled, with physical considerations yielding insight into the underlying mathematics and vice versa. This often requires the use of tools and concepts from diverse areas of mathematics ranging from analysis, differential equations, geometry, and topology to numerical analysis and continuum physics.

One main area of interest has been to study the existence and properties of singular energy minimisers and their connection with fracture mechanisms observed in polymers. A key problem here, on which I have been working, is to develop new numerical approaches to predicting the formation and location of singularities.

A more recent interest has been to understand the connections between my previous studies in nonlinear elasticity and corresponding phenomena in fluid mechanics.

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Projects 2008 2016

Research Output 1986 2018

3 Citations (Scopus)

On the Uniqueness of Energy Minimizers in Finite Elasticity

Sivaloganathan, J. & Spector, S. J., 5 Feb 2018, In : Journal of Elasticity. p. 1 - 31 31 p.

Research output: Contribution to journalArticle

Open Access
File
Elasticity
Boundary conditions
Derivatives
1 Citations (Scopus)

On the global stability of compressible elastic cylinders in tension

Sivaloganathan, J. & Spector, S. J., Aug 2015, In : Journal of Elasticity. 120, 2, p. 161-195 31 p.

Research output: Contribution to journalArticle

Open Access
File
Shear bands
Boundary conditions
1 Citations (Scopus)

A characterisation of the boundary displacements which induce cavitation in an elastic body

Negron-Marrero, P. V. & Sivaloganathan, J., 1 Sep 2012, In : Journal of Elasticity. 109, 1, p. 1-33 33 p.

Research output: Contribution to journalArticle

Cavitation
Boundary conditions
Derivatives
Elasticity
Fluids
6 Citations (Scopus)

Aspects of the nonlinear theory of type II thermoelastostatics

Quintanilla, R. & Sivaloganathan, J., Mar 2012, In : European Journal of Mechanics - A/Solids. 32, 1, p. 109-117 9 p.

Research output: Contribution to journalArticle

thermoelasticity
Thermoelasticity
uniqueness
Free energy
free energy
1 Citations (Scopus)

On the relative energies of the Rivlin and cavitation instabilities for compressible materials

Lloyd, J. G. & Sivaloganathan, J., 1 Jun 2012, In : Mathematics and Mechanics of Solids. 17, 4, p. 338-350

Research output: Contribution to journalArticle

Open Access
File
Cavitation
Energy
Minimizer
Cavity
Ball