Complex Deformations of Biological Soft Tissues

该项目是一个研究项目的一部分，旨在了解生物软组织（如肌腱和肌肉）的微观结构如何影响它们的大规模机械性能。特别是，我们希望了解微观结构的变化，可能是由于疾病，如何影响组织的功能。该项目将涉及使用和本构定律的发展，以描述整个组织的机械行为，明确包含微观结构特征。该领域之前的大部分工作都集中在通过简单变形（例如简单形状在张力下的纵向延伸或“拉进一条直线”）来测试本构模型，可以找到精确的解析解。然而，在人体中，几何和机械环境要复杂得多。学生采取的方法将是计算和分析。首先，学生将在我们的“内部”有限元库oomph-lib中实现由联合导师最近开发的肌腱本构律。然后，他将计算结果与简单变形的解析解进行比较。在验证了本构定律的实现后，本构定律将应用于更现实的（复杂的）几何形状和加载条件，以探索它们在体内模拟肌腱的能力。我们预计本构定律的进一步发展将需要他们提供一个准确的肌腱力学模型。扩展到其他软组织和不同的几何形状将探索博士的进展。这项研究是在连续介质力学领域，将需要开发新的软组织本构定律和非标准连续介质力学问题的公式和解决方案。研究工作也属于“生物物理学和软物质物理学”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".