Stress and Strain Tensor (Continued) and Cauchy Formula for Traction — Lesson 2

This lesson covers the concept of tensors, their orders, and their applications in physics and engineering. It explains the difference between scalar, vector, and tensor quantities, and provides examples of each. The lesson further delves into the concept of stress as a tensor and explains how to define the order or rank of a tensor. It also discusses the representation of tensors using symbols and indices. The lesson then moves on to the topic of strain, explaining how to quantify deformation at a point and define strains. It provides a detailed explanation of how to calculate strains in different directions and introduces the concept of shear strain. The lesson concludes with a discussion on the equilibrium equations in different directions and the Cauchy formula for calculating traction on any arbitrary plane.

Video Highlights

02:15 - Explanation of the order or rank of a tensor
06:28 - Explanation of how to quantify deformation at a point or define strains
09:15 - Detailed calculation of strains in x and y directions
20:41 - Explanation of shear strain and its calculation
27:46 - Discussion on the convention for positive and negative strain
43:46 - Explanation of traction on any arbitrary plane and Cauchy formula

Key Takeaways

- Tensors are a more general quantity used in physics and engineering, with scalar and vector being specific types of tensors.
- The order or rank of a tensor is defined by the number of attributes it has.
- Stress is a second rank tensor, having magnitude, direction of action, and a plane of association.
- Strain quantifies the deformation at a point and can be calculated in different directions.
- Shear strain is defined as the change in the angle between two orthogonal directions under the action of external loading.
- The Cauchy formula allows for the calculation of traction on any arbitrary plane if the direction cosines of the plane and the stresses at a point are known.