Complex Deformations of Biological Soft Tissues

This project is part of a research programme designed to understand how the microstructure of biological soft tissues (e.g. tendons and muscles) affects their large-scale mechanical properties. In particular, we wish to understand how changes in the microstructure, perhaps due to disease, affect the function of the tissue. This project will involve the use and development of constitutive laws to describe the mechanical behaviour of the whole tissue with explicit inclusion of microstructural features. The majority of the previous work in this area has focused on testing the constitutive models via simple deformations (e.g. longitudinal extension of simple shapes under tension or "pulling in a straight line") for which exact analytical solutions can be found. In the body, however, the geometry and mechanical environments are much more complex.
The approach taken by the student will be both computational and analytical. Initially, the student will implement the constitutive laws for tendons recently developed by the Co-supervisor in our "in house" finite element libraray oomph-lib. He will then compare computational results against the analytic solution for the simple deformations. Having thus validated the implementation the constitutive laws will be applied in more realistic (complex) geometries and loading conditions in order to explore their ability to model the tendons in vivo. We anticipate that further development of the constitutive laws will be required for them to provide an accurate model of tendon mechanics. Extensions to other soft tissues and different geometries will be explored as the PhD progresses.
This research is in the area of Continuum Mechanics and will require the development of novel constitutive laws for soft tissues and the formulation and solution of non-standard continuum mechanics problems. The work also falls within "Biophysics and Soft Matter Physics" and "Mathematical Biology".