# What is Kirchhoff stress?

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## What is Kirchhoff stress?

The components of the first Piola-Kirchhoff stress are the forces acting on the deformed configuration, per unit undeformed area. They are thought of as acting on the undeformed solid . Evidently, if we choose F as our deformation measure, the appropriate generalized force is the first Piola-Kirchhoff stress S.

## Is Cauchy stress True stress?

Stress Measures. The most fundamental and commonly used stress quantity is the Cauchy stress, also known as the true stress. It is defined by studying the forces acting on an infinitesimal area element in the deformed body. Both the force components and the normal to the area have fixed directions in space.

Is second Piola-Kirchhoff stress tensor symmetric?

Second Piola-Kirchoff tensor is symmetric but 1st piola is not , which gives advantages in computation.

### What is stress power?

For an elastic material, the stress power is the rate of change of the strain energy density. By using the relations. the stress power can be represented in the following equivalent form: Thus, we can say that the first Piola-Kirchhoff stress tensor and the deformation gradient form an energy conjugate pair.

### What is nominal stress?

Stress calculated on the basis of the net cross section of a specimen without taking into account the effect of geometric discontinuities such as holes, grooves, fillets, etc.

What is normal stress?

A normal stress is a stress that occurs when a member is loaded by an axial force. The value of the normal force for any prismatic section is simply the force divided by the cross sectional area. A normal stress will occur when a member is placed in tension or compression.

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## When does the Piola Kirchhoff stress tensor remain constant?

If the material rotates without a change in stress state (rigid rotation), the components of the 2nd Piola–Kirchhoff stress tensor remain constant, irrespective of material orientation. The 2nd Piola–Kirchhoff stress tensor is energy conjugate to the Green–Lagrange finite strain tensor.

Is the pK1 stress tensor symmetric with Cauchy stress?

PK1 stress (3.5.8) The Cauchy stress is symmetric, but the deformation gradient is not. Hence the PK1 stress tensor is not symmetric, and this restricts its use as an alternative stress measure to the Cauchy stress measure.

### Which is a physical interpretation of Cauchy stress?

1) We know that Cauchy stress involved deformed areas-therefore this (Cauchy stress) has an obvious physical interpretation where, J is the jacobian of the deformation gradient which physically is the measure of the volume change produced by a deformation. sigma is Cauchy stress.

### Why do we need to introduce strange measures of stress?

The second Piola-Kirchhoff stress has no obvious physical interpretation. So why do we need to introduce these strange measures of stress? They are perhaps best thought of as generalized forces, in the sense of Lagrangean mechanics.