My work lies at the interface between mathematics and solid mechanics, mechanical / aerospace engineering and biology.
Specific areas of interest in solid mechanics include microstructure formation and evolution, especially in multiphase solids and superalloys; damage; and polycrystals. On the biological side I am interested in tissue mechanics, especially growth; plant mechanics and viral mechanics. Viral mechanics has also been the inspiration for my research on morphing structures with engineering collaborators.
Specific areas of interest in solid mechanics include microstructure formation and evolution, especially in multiphase solids and superalloys; damage; and polycrystals. On the biological side I am interested in tissue mechanics, especially growth; plant mechanics and viral mechanics. Viral mechanics has also been the inspiration for my research on morphing structures with engineering collaborators.
Ongoing Research
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Plant Mechanics
Tanniemola Liverpool, Claire Grierson with her group, and I are seeking to understand plant uprooting, and together with Timothy Quine and his group to model the effect of root hairs on soil erosion. |
Multiphase Solids
I am working on a geometric understanding of the phenomenon of supercompatibility (identified by Richard D. James), and, together with Georgy Kitavtsev, on extending it to thin-films. |
Viral Mechanics
Walter Whiteley, Antony Nixon and I are attempting to bring together ideas from combinatorial rigidity and mechanics to understand the mechanism of the tail sheath of the virus Bacteriophage T4. |
Recent Research
Morphing StructuresThese are (typically composite) structures that exploit subtle interplay between geometry and mechanics.
Morphing shell structures: A generalised modelling approach
(with Ettore Lamacchia, Alberto Pirrera and Paul Weaver) Composite Structures, 131, 1017-1027 November 2015 Non-axisymmetric bending of thin annular plates due to circumferentially distributed moments
(with Ettore Lamacchia, Alberto Pirrera and Paul Weaver) International Journal of Solids and Structures, 51 (3–4), 622-632 February 2014 |
DamageChristopher Larsen and I have recently proposed energetic and strain-threshold models for the quasi-static evolution of brutal brittle damage for geometrically-linear elastic materials. By allowing for anisotropic elastic moduli and multiple damaged states we present the issues for the first time in a truly elastic setting. This research was funded by the Leverhulme Trust.
Quasi-static brittle damage evolution in elastic materials with multiple damaged states
Archive for Rational Mechanics and Analysis, 215(3), 831-866 March 2015 |
MorphoelasticityMathematical models of biological growth commonly attempt to distinguish deformation due to growth from that due to mechanical stresses through a hypothesised multiplicative decomposition of the deformation gradient. Shifting the focus to the mechanical energy of the growing object, Patrick Shipman and I propose an 'energy-deformation decomposition' which accurately captures the influence of growth on mechanical energy for tissues with crystalline structure. Our arguments also apply to tissues with a network structure.
An energy-deformation decomposition for morphoelasticity
Journal of the Mechanics and Physics of Solids, 67, 15-39 July 2014 |
SuperalloysThomas Blesgen and I have proposed a two-scale model that attempts to rigourously include both elasticity and diffusion for coarsening in superalloys, which are used in turbine blades. The microstructure of these materials evolves through a elasticity-influenced diffusion.
Cahn-Hilliard equations incorporating elasticity: Analysis and comparison to experiments
Philosophical Transactions of the Royal Society A, 371(2005), 20120342 November 2013 A generalised Cahn-Hilliard equation incorporating geometrically linear elasticity
Interfaces and Free Boundaries, 13(1), 1-27 2011 |
Bio-Inspired MechanicsI am interested in the design and analysis of engineered structures that are inspired by the behaviour of biological structures. We have prototyped a bistable cylindrical lattice structure that mimics the behaviour of the virus Bacteriophage T4.
Multi-stable cylindrical lattices
(with Alberto Pirrera, Xavier Lachenal, Stephen Daynes and Paul Weaver) Journal of the Mechanics and Physics of Solids, 61(11), 2087–107 November 2013 |
Multiphase SolidsAnja Schloemerkemper and I have shown that monoclinic-i martensite is capable of exhibiting an open set of T3 microstructures. This is the first 'real-world' example of these theoretically much-investigated microstructures.
We also show that there are in fact two kinds of monoclinic-i martensites, group-theoretically indistinguishable but with different convex polytope structures, and thus also different semi-convex hulls/envelopes. Curiously all known monoclinic-i martensites lie in one of these groups. This research was funded by the Royal Society. Non-laminate microstructures in monoclinic-i martensite
Archive for Rational Mechanics and Analysis, 207(1), 39-74 January 2013 |
