Nonlinear elasticity theory
My main research interests are in nonlinear elasticity theory, including both fundamental theoretical work and a variety of applications. Publications include my book Non-Linear Elastic Deformations (Ellis Horwood, 1984, and Dover, 1997), available from Amazon.co.uk or Amazon.com.
Recent work has been concerned with the derivation of new classes of exact solutions for boundary-value problems for compressible elastic solids, with my students Xiamei Jiang, Eleftherios Kirkinis and Fotios Kassianidis.
Linear and nonlinear stability analysis of pre-stressed elastic bodies, in collaboration with Professor Yibin Fu, Keele University, has also been a feature of my work in the last few years. With Yibin Fu I edited the volume Nonlinear Elasticity: Theory and Applications, published by Cambridge University Press.
Other collaborators in different aspects of nonlinear elasticity include Dr. David Haughton, Glasgow, and Professor Jim Haddow, University of Victoria.
Mechanics of rubberlike solids
I have been concerned with modelling the elastic response of rubberlike solids through the development of strain-energy functions, which have subsequently been used both in theoretical analysis and in many engineering applications. In particular, they have been incorporated into several commercial Finite Element software packages, including ABAQUS, ALGOR, ADINA, ANSYS, LS-DYNA and MARC, used by engineers, particularly in the aerospace and automotive industries.
Recent work on inelastic effects in rubber (such as stress softening and residual strains) has been based on a theory of pseudo-elasticityand has been funded by the UK Engineering and Physical Sciences Research Council (EPSRC). The research has also been supported by the Tun Abdul Razak Research Centre (TARRC) of the Malaysian Rubber Producers’ Research Association (MRPRA) and by Pirelli Pneumatici, Milan. A version of the pseudo-elastic model is now implemented in ABAQUS and ADINA.
Collaborators include Dr. David Roxburgh, University of Newcastle upon Tyne, Dr. Luis Dorfmann, Tufts University, Professor Giuseppe Saccomandi and Dr. Ivonne Sgura, University of Lecce, and Professor Niall Horgan, University of Virginia.
A project on elastomeric structures in the context of virtual vehicle design in collaboration with Professor Gerhard Holzapfel (Graz University of Technology, Austria) was started in 2003.
The research on rubberlike materials also relates to damage mechanics: in particular, work on pseudo-elastic modelling of changes in material properties induced by damage has been conducted in collaboration with Professor Kostas Lazopoulos at the National Technical University of Athens.
In September 2002, Giuseppe Saccomandi and I organized an Advanced Course on the Mechanics and Thermomechanics of Rubberlike Solids at the International Centre for Mechanical Sciences (CISM), Udine, Italy. The lecture notes from this course were published in the CISM Courses and Lectures series (Volume 452) in 2004.
Biomechanics of soft tissue
A major new interest is in the mechanics of biological tissues: in
particular,
phenomenological and structural modelling of the mechanical response of
arterial walls, in collaboration with Professor
Gerhard Holzapfel and the biomechanics group at Graz University of
Technology, Austria. This collaboration is currently supported by
a grant from the Royal Society. An anisotropic material model
that we published
in the Journal
of Elasticity in 2000 has recently been implemented in ADINA.
With Gerhard Holzapfel I ran an Advanced
Course on the Biomechanics of Soft Tissue at the International
Centre
for Mechanical Sciences (CISM), Udine,
Italy in September 2001. The lectures from the course have been
published
in the CISM Courses and Lectures series (Volume 441, 2003).
Another course, a joint IUTAM/CISM Summer School, will be held in Udine
in September 2006.
Another important activity in this area was an IUTAM Symposium on Mechanics of Biological Tissue, which was held in Graz, Austria, from June 27 to July 2, 2004. The proceedings of this Symposium were published by Springer early in 2006.
Surface mechanics
With Professor David Steigmann, University of California, Berkeley, I have been involved in the development of a theory of thin-film elastic surface coating of finitely deformed elastic solids, including the associated stability theory and study of the influence of thin films on elastic wave propagation.
Thermoelasticity and heat conduction
Work on thermoelastic modelling under large temperature changes and heat conduction effects is in progress in collaboration with Professor Jim Dunwoody at Queen's University, Belfast (funded by EPSRC).
Mechanics of fibre-reinforced solids
A recently developed interest is the modelling of fibre-reinforced solids under large strains, particularly with reference to questions of stability and failure mechanisms. This work is conducted in collaboration with Professor Tom Pence, Michigan State University, and Dr. José Merodio, University of Cantabria. José Merodio and I ran a Summer School on Nonlinear elasticity, constitutive equations and the characterization of material properties, with applications to composites and biomechanics in Laredo, Spain, in August 2003. In September 2004 we organized a Euromech Colloquium on Fibre-reinforced Solids: Constitutive Laws and Instabilities, in Castro Urdiales, Cantabria, Spain.
Wave propagation in pre-stressed elastic solids
A continuing interest is the analysis of the effect of pre-stress
and
finite deformation on the propagation of waves in elastic solids and
related
questions of stability. This has involved collaboration with Professor
Dimitrios Sotiropoulos in the Technical University of Crete, and
Professor
Adriano Montanaro at the University of Padua, and, more
recently,
Dr. Michel Destrade, University Pierre and
Marie Curie, Paris.
Other work on elastic waves has been conducted jointly with Professor
Włodek
Domański, of
the Polish Academy of Sciences, Warsaw.
Professor Giuseppe Saccomandi, University of Lecce, and I have developed this type of analysis for viscoelastic material response.
Nonconvex problems in solid mechanics
In collaboration with Professor David Gao, Virginia Tech, I have been concerned with some aspects of the application of nonconvex analysis to problems in nonlinear elasticity.
Nonlinear magnetoelasticity and electroelasticity
Dr. Luis Dorfmann, Tufts University and
I have recently become involved in the application of
nonlinear
magnetoelasticity theory in the modelling of magneto-sensitive
elastomers, and in the mechanics of electroelastic materials in
conjunction with my student Roger Bustamante.
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Page last updated 13 April 2006