Solid Mechanics in Cardiovascular Fluid Mechanics — Lesson 3

This lesson covers the fundamental concepts of solid mechanics, particularly as they apply to cardiovascular fluid mechanics. It begins with a review of basic solid mechanics concepts learned in the first year of undergraduate engineering courses. The lesson then delves into the unique characteristics of flow in the cardiovascular system, emphasizing the flexible nature of the tubes (arteries and veins) in which the flow occurs. The lesson further explains the stress-strain relationship in solid walls, the concept of elastic materials, and the definitions of normal stress, strain, and elastic modulus. It also discusses the behavior of ductile and brittle materials, the concept of engineering strain, and the definition of Poisson's ratio. The lesson concludes with an analysis of shear stress and strain, the generalized Hooke's law, and the concept of bulk modulus as well as a comprehensive analysis of thin-walled and thick-walled tubes in a cardiovascular system.

Video Highlights

01:57 - Discussion on stress-strain relationship in solid walls
04:03 - Explanation of normal stress, strain, and elastic modulus
07:20 - Explanation of engineering strain and true strain
11:41 - Definition of Poisson's ratio
17:27 - Explanation of generalized Hooke's law
22:38 - Discussion on bulk modulus
27:05 - Analysis of thin-walled tubes in cardiovascular system
38:40 - Analysis of thick-walled tubes in cardiovascular system

Key Takeaways

- The cardiovascular system's flow occurs in flexible tubes (arteries and veins), making the understanding of solid mechanics crucial.
- Elastic materials deform when a force is applied and return to their original configuration once the force is removed.
- The stress-strain relationship in solid walls significantly impacts the flow behavior in the cardiovascular system.
- The Poisson's ratio, which is the ratio of transverse strain to axial strain, plays a significant role in understanding the deformation of materials.
- The shear stress and strain, along with the generalized Hooke's law, provide a comprehensive understanding of how materials behave under different forces.
- The bulk modulus, which measures a substance's resistance to uniform compression, is a key concept in understanding the behavior of materials under pressure.