Solid Mechanics research is an area of vital importance in many branches of engineering, geophysics, and material science. The subject continues to develop at a rapid rate as new materials and designs are introduced to meet the stringent demands of industry; the latter requirements may include the need for lightness, strength, heat resistance etc. Theoretical study by applied mathematicians is essential to advance the understanding of the fundamental mechanical and dynamical properties of such materials, to provide new mathematical tools and insights into the field, and of course to estimate the potential for fracture or other catastrophic failure in situ . Such theoretical work also offers novel approaches to anticipating the behaviour of ever-more-complex materials being employed by material scientists, especially in the field of nanotechnology and metamaterials.
The use of solid mechanics in order to understand various biomechanics problems has become very important recently. This has included applications in order to understand the constitutive response of soft and hard tissues as well as buckling problems in order to understand airway re-opening.
A wide variety of research into various aspects of solid mechanics takes place within the School of Mathematics at Manchester. This involves a blend of theoretical, numerical and experimental work. Much of this is interdisciplinary involving collaborations with the Schools of Engineering, Materials Science and Physics in Manchester as well as other universities around the globe as well as industrial collaborators, recent examples of which have included Thales Underwater Systems, Cadburys and BP.
The most straightforward constitutive model in solid mechanics is that of Hookean (linear) elasticity. This can involve either static or dynamic loadings, the latter leading to the subject of elastodynamics, i.e. elastic wave propagation. Much of the work in this area at Manchester takes place within the Waves In Complex Continua group, led by Abrahams and Parnell. This work includes models of waves in complex composite materials and bone. A subject of great importance presently is that of homogenization and micromechanics. These present techniques to upscale material properties so that macroscopic constitutive models can be developed from the knowledge of the (possibly hierarchical) microstructure of a complex material.
Further work in the area of biological media has been conducted by the Scientific Computing group at Manchester, led by Hazel and Heil. This has involved developing an in-house finite element software package (oomph-lib) in order to model e.g. the buckling of thin cylindrical shells subject to dynamic loading, with applications in airway opening and re-opening. These problems are particularly difficult due to the complex fluid-structure interaction as well as nonlinearity due to large displacements of the shell wall.
Various collaborative work has recently taken place between members of the Scientific Computing and Waves In Complex Continua groups. This has focused in particular on the modelling of linear elastic composite materials and wave propagation in complex geometries.
Nonlinear materials are present in many everyday scenarios. Soft biological tissue behaves in a constitutively nonlinear manner, i.e. it is not a Hookean materials. Furthermore all manner of rubber based composites are used in industry. The nonlinearity of such materials presents a variety of advantages. As well as modelling such composites in the context of the Waves In Complex Continua a significant amount of experimental work is carried out, particularly that led by Juel within the Manchester Centre for Nonlinear Dynamics. Links between the Experimental Group and the Scientific Computing group are strong, motivated by the need to model such complicated experiments computationally.
An interesting aspect of solid mechanics is the ability to describe the deformation and flow of granular materials. The Granular materials group at Manchester, led by Gray and Harris. is particularly interested on the dense regime in which the grains behave either as a solid or a liquid. As should be expected, there are numerous applications of this theory including understanding slow flows in silos and hoppers, predicting the flows of avalanches, as well as to problems in the food science and pharmaceutical industries.