For an anisotropic, elastic medium with elastic energy density integrate this energy density over a 3 dimensional region V (not necessarily small) to get the total elastic energy E Now consider a small variation i in the displacement field Evaluate the resulting change E in the elastic energy without using the relation Convert to a surface integral over V, and thence infer the stress strain relation U i j Yijkl k l

Question: For an anisotropic, elastic medium with elastic energy density integrate this energy density over a 3-dimensional region V (not necessarily small) to get the total

For an anisotropic, elastic medium with elastic energy density

integrate this energy density over a 3-dimensional region V (not necessarily small) to get the total elastic energy E. Now consider a small variation δξ_i in the displacement field. Evaluate the resulting change δE in the elastic energy without using the relation

Convert to a surface integral over ∂V, and thence infer the stress strain relation

U = i;j Yijkl k;l>

Step by Step Solution

★★★★★

3.40 Rating (147 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

To evaluate the change in elastic energy due to a small variation in the displacement field we can u... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Modern Classical Physics Questions!

List three specific parts of the Case Guide, Objectives and Strategy Section (See below) that you had the most difficulty understanding. Describe your current understanding of these parts. Provide...

Planning is one of the most important management functions in any business. A front office managers first step in planning should involve determine the departments goals. Planning also includes...

A tank with an internal volume of 1 m3 contains air at 800 kPa and 25C. A valve on the tank is opened allowing air to escape and the pressure inside quickly drops to 150 kPa, at which point the valve...

Derive the energy-density, energy-flux, and lagrangian properties of elastodynamic waves given in Sec. 12.2.5. Specifically, do the following. (a) For ease of calculation (and for greater...

Volkswagen shocked the world on September 18, 2015 with its response to the U.S. Environmental Protection Agency's (EPA) notice that Volkswagen's "clean diesel" vehicles were found to be in violation...

Using "A Dynamical Theory of the Electromagnetic Field" by Clerk Maxwell -What is the main idea of the Author's argument? What is the main essence of the piece? -What ways does the author use to...

1. What makes Nagesh Battula entrepreneurial? Is the opportunity of eco-habitats a large enough opportunity? 2. What makes Project Damergidda different? What should be Organo's marketing strategy for...

Wave Energy and Intensity Waves aves transfer energy from one location to another. As the wave propagates the particles in a dense elastic transmitting medium perform simple harmonic motion about...

The experimental result differs from the assumption. The result shows that the ring oscillator frequencies can be grouped into two groups, where the first group is the high frequency group for the...

Summarize this for me Someone who understand MEA and HEA very well. And please make sure the summary is 2 pages . no less than 2 pages plz thanks Effects of temperature on mechanical properties and...

Compare and explain the very different locations of decomposers and producers.

1. Give examples of the following kinds of relationships. Do not use examples already provided in the text or by your professor. Positive relationship Negative relationship Two variables that you...

Which of the following is the best description of the process of analyzing the meaning of the Tsotsil ( aka Tzotzil ) Maya word nichim? Question 7 options: Syntax. Semantics. Phonetics...

=+a. What is the value of the sample correlation coefficient r?

A particle moves along the x-axis while acted on by a single conservative force parallel to the x-axis. The force corresponds to the potential-energy function graphed in Fig. P7.86. The particle is...

The mass of a regulation tennis ball is 57 g (although it can vary slightly), and tests have shown that the ball is in contact with the tennis racket for 30 ms. (This number can also vary, depending...

Experimental tests have shown that bone will rupture if it is subjected to a force density of 1.03 10 8 N/m 2 . Suppose a 70.0-kg person carelessly rollerskates into an overhead metal beam that hits...

2. Distinguish between absolute and reasonable assurance. Identify the type of assurance that is expected in an audit of the financial statements, clearly outlining the reasons to justify your point...

You have the following information for Monty Inc. for the month ended October 31, 2022. Monty uses a periodic method for inventory. Weighted-average cost per unit $ (2) FIFO. (3) Average-cost. (Round...

Assume that on April 1 , Jerome, Inc., paid $ 1 0 0 , 0 0 0 to buy Potter's 8 percent, two - year bonds with a $ 1 0 0 , 0 0 0 par value. The bonds pay interest semiannually on March 3 1 and...