Relation between Elastic Constants and Strain Energy Densities - Lesson 2

This lesson covers the relationship between elastic constants such as modulus of elasticity, Poisson's ratio, and modulus of rigidity. It explains how these constants are interrelated in isotropic materials. The lesson also introduces another elastic constant, the bulk modulus, and shows how it is related to the modulus of elasticity and Poisson's ratio. The lesson further delves into the concept of strain energy, explaining how it is calculated in one, two, and three dimensions. It also discusses the concept of volumetric and distortion energy densities, and how they relate to the principle stresses at a point.

Video Highlights

00:40 - Introduction to the relationship between elastic constants.
06:17 - Explanation of the concept of normal strain and its calculation
20:18 - Calculation of strain energy in one dimension.
25:29 - Calculation of strain energy in two dimensions.
36:16 - Calculation of strain energy in three dimensions.
41:55 - Calculation of volumetric strain energy density.
44:38 - Calculation of distortion energy density
53:40 - Explanation of the Mohr circle diagram and its implications

Key Takeaways

- Elastic constants like modulus of elasticity, Poisson's ratio, and modulus of rigidity are interrelated in isotropic materials.
- The bulk modulus is another elastic constant that is related to the modulus of elasticity and Poisson's ratio.
- Strain energy can be calculated in one, two, and three dimensions.
- The total strain energy density can be split into volumetric and distortion energy densities.
- The change in volume due to the deviatory part of the stress component is zero.