Stress tensor : tension VS Pressure

In summary, tension and pressure are two types of stress in a material, with tension being a pulling force and pressure being a pushing force. In a stress tensor, tension is represented by positive values and pressure by negative values. Tension can occur in different directions in a material, depending on the direction of the applied force, and is represented by the corresponding stress component in a stress tensor. Tension and pressure can coexist in a material, and this is accounted for in a stress tensor by having both positive and negative values for different stress components. In addition to tension and pressure, a stress tensor also includes components for shear stress, which occurs when a material is subjected to forces that cause one part to slide or shift relative to another part.
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zn52
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My question is regarding exercise 5.1 on page 141 of MTW. How come the tension and the pressure have the same value ? The field lines here are they the field lines of the electromagnetic force ?
Thanks,
 
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1. What is the difference between tension and pressure in a stress tensor?

Tension and pressure are two types of stress that occur in a material. Tension is a pulling force that causes a material to elongate, while pressure is a pushing force that causes a material to compress. In a stress tensor, tension is represented by positive values and pressure by negative values.

2. How is tension related to the direction of stress in a material?

Tension can occur in different directions in a material, depending on the direction of the applied force. For example, if a force is applied along the x-axis, tension will occur in the x-direction. In a stress tensor, the direction of tension is represented by the direction of the corresponding stress component.

3. Can tension and pressure coexist in a material?

Yes, tension and pressure can coexist in a material. In fact, most materials experience a combination of both tension and pressure in different areas. This is represented in a stress tensor by having both positive and negative values for different stress components.

4. How does a stress tensor account for shear stress?

In addition to tension and pressure, a stress tensor also includes components for shear stress. Shear stress occurs when a material is subjected to forces that cause one part of the material to slide or shift relative to another part. This is represented in a stress tensor by off-diagonal components.

5. What is the significance of understanding tension and pressure in a stress tensor?

Understanding tension and pressure in a stress tensor is crucial for analyzing the mechanical behavior of materials. It allows scientists to predict how a material will respond to external forces and how it will deform under stress. This information is used in various engineering applications, such as designing structures and machines, to ensure their safety and durability.

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