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Department of Mathematics

Solid mechanics and soft matter

Predicting the responses of solid substances to imposed loads is of vital importance in engineering, geophysics, and material science. Soft matter is the sub-set of materials that deform easily subject to relatively small loads, including for example gels, foams and a number of biological materials.

Solid mechanics and soft matter research within the Department of Mathematics at Manchester involves a blend of theoretical, numerical and experimental work. Much of the work is interdisciplinary and many of the  experiments are conducted within the solid-mechanics laboratory run by the Manchester Centre for Nonlinear Dynamics. Our collaborators include the School of Engineering, and the Departments of Materials and Physics in Manchester; other universities around the globe; and industrial companies,  such as  Thales UK and Mondelez.

Our solid mechanics research includes the development of constitutive laws based on rational micromechanical models and homogenisation techniques. This field provides mathematical tools to  upscale material properties so that macroscopic constitutive models can be developed from the knowledge of the (possibly hierarchical) microstructure of a complex biological or synthetic material. The most straightforward constitutive model in solid mechanics is that of Hookean (linear) elasticity, appropriate for small deformations. Soft materials, such as biological soft tissue, chocolate, gels and foams,  that deform easily (and possibly flow) have more complex (nonlinear) constitutive behaviours that remain incompletely understood and are a current area of focus.

Our research also includes the study of the large-scale response of solid materials to applied loads and how that response changes with the constitutive behaviour of the material.  The loading can be static or dynamic, the former leading to our investigations of the buckling of sheets, cylinders or solids with complex geometries; and the latter leading to the subject of elastodynamics, or elastic wave propagation, a focus area of the Waves and Metamaterials group. In many applications, such as airway reopening, the loading is provided by a surrounding fluid whose behaviour is in turn dictated by the motion of the solid. These fluid-structure interaction problems are particularly challenging and exhibit a wide variety of nonlinear behaviours.

More information about our research, and some papers, can be found by browsing the webpages of academic staff members. Potential PhD students may email staff directly to discuss possible projects.