In this video, Constitutive Relationship between Stress and Strain is explained in following timestamps:
0:00 – Mechanics of Solid Lecture series
0:18 – Outlines on the session
0:53 – Constitutive Relationship between Stress and Strain for One Dimensional Stress System
2:45 – Constitutive Relationship between Stress and Strain for Two-Dimensional Stress System
7:06 – Constitutive Relationship between Stress and Strain for Three-Dimensional Stress System

Following points are covered in this video:
1. Constitutive Relationship between Stress and Strain for One Dimensional Stress System
2. Constitutive Relationship between Stress and Strain for Two Dimensional Stress System
3. Constitutive Relationship between Stress and Strain for Three Dimensional Stress System

Engineering Funda channel is all about Engineering and Technology. Here this video is a part of Mechanics of Solids and Engineering Mechanics.

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Details of Constitutive Relationship between Stress and Strain:

The constitutive relationship between stress and strain is a fundamental concept in materials science and engineering. It describes the relationship between the stress applied to a material and the resulting strain, or deformation, of the material.

There are many constitutive models that can be used to describe the stress-strain behavior of materials, but one of the most common and simple models is the linear elastic model. According to this model, stress is directly proportional to strain in the elastic region of a material. This relationship is known as Hooke's law, and it can be expressed as:

σ = Eε

where σ is the stress, E is the modulus of elasticity (also known as Young's modulus), and ε is the strain.

This relationship holds true for materials that exhibit linear elastic behavior, meaning that they behave elastically under small deformations, up to a certain point known as the elastic limit. At the elastic limit, the material undergoes plastic deformation, and the relationship between stress and strain becomes nonlinear.

Other constitutive models, such as the nonlinear elastic model, the viscoelastic model, and the plasticity model, can be used to describe the stress-strain behavior of materials beyond the elastic limit. These models are more complex and require more parameters to fully describe the behavior of a material under load.

In summary, the constitutive relationship between stress and strain describes the relationship between the stress applied to a material and the resulting deformation of the material. The linear elastic model, described by Hooke's law, is a simple and common model that holds true for materials that exhibit linear elastic behavior under small deformations. Other constitutive models can be used to describe the behavior of materials beyond the elastic limit.