Complex Deformations of Biological Soft Tissues

该项目是旨在了解生物软组织(例如肌腱和肌肉)的微结构如何影响其大规模机械性能的研究方案的一部分。特别是，我们希望了解微结构的变化，可能是由于疾病，如何影响组织的功能。这个项目将涉及使用和开发本构定律来描述整个组织的力学行为，并明确包含微观结构特征。以前在这一领域的大部分工作都集中在通过简单的变形(例如，简单形状在拉伸下的纵向延伸或“拉入直线”)来测试本构模型，对于这些变形可以找到精确的解析解。然而，在人体内，几何和机械环境要复杂得多。学生采取的方法将是计算性和解析性的。首先，学生将在我们的“内部”有限单元库中实施共同导师最近开发的肌腱本构定律。然后，他会将计算结果与简单变形的解析解进行比较。在验证了实现后，本构定律将应用于更真实(复杂)的几何和载荷条件，以探索它们在体内模拟肌腱的能力。我们预计，需要进一步发展本构定律，以便为肌腱力学提供准确的模型。随着PHD的发展，将探索扩展到其他软组织和不同几何形状。这项研究是在连续统力学领域，需要发展新的软组织本构关系，以及非标准连续统力学问题的公式和解决方案。这项工作也属于《生物物理学与软物质物理学》和《数学生物学》。

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".