Chapter 10: Q5P (page 520)

Show by the quotient rule (Section 3 ) that $C_{ijkm}$ in $(7.5)$ is a $4^{th}$ -rank tensor.

Short Answer

Expert verified

The statement has been proven.

Step by step solution

Given Information

The tensor $C_{i j k m}$ .

Definition of a strain tensor.

Solids are strained under applied forces, resulting in a change in volume and shape is called strain tensor.

Verify the statement.

The tensor $C_{i j k m}$ .

Let S is the strain tensor.

Correspondence between point mechanics and mechanics of an elastic body.

$r \leftrightarrow s F = - \nabla U \leftrightarrow P F = m a \leftrightarrow P_{i j} F = C_{i j k l} S_{k l}$

In the above statement $P_{i j} = C_{i j k l} S_{k l}$

C is a fourth rank tensor.

Hence, the statement has been proven.

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Show by the quotient rule (Section 3 ) that $C_{ijkm}$ in $(7.5)$ is a $4^{th}$ -rank tensor.

Short Answer

Step by step solution

Given Information

Definition of a strain tensor.

Verify the statement.

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Show by the quotient rule (Section 3 ) that Cijkmin (7.5)is a 4th-rank tensor.

Short Answer

Step by step solution

Given Information

Definition of a strain tensor.

Verify the statement.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

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Show by the quotient rule (Section 3 ) that $C_{ijkm}$ in $(7.5)$ is a $4^{th}$ -rank tensor.