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Easy Elasticity Theory

Friday, April 23, 2010. Hooke's law in component form. We start with Hooke's law for the strain tensor, and then substitute the E and nu. Material properties for K and mu. We see that there is still a compression term, now on the right, but not a pure shear term, and both terms contain both material constants. We mention here that nu. The shear modulus is about is about 40 % of the Young's modulus. The bulk modulus (of compression) is therefore about 1.5 to 2 times larger than the shear modulus. The shea...

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Easy Elasticity Theory | baergblog.blogspot.com Reviews

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Friday, April 23, 2010. Hooke's law in component form. We start with Hooke's law for the strain tensor, and then substitute the E and nu. Material properties for K and mu. We see that there is still a compression term, now on the right, but not a pure shear term, and both terms contain both material constants. We mention here that nu. The shear modulus is about is about 40 % of the Young's modulus. The bulk modulus (of compression) is therefore about 1.5 to 2 times larger than the shear modulus. The shea...

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1 easy elasticity theory

2 the result is

3 or k

4 or mu

5 and sigma/e

6 and mu

7 posted by

8 bill baerg

9 no comments

10 labels poissons ratio

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Easy Elasticity Theory | baergblog.blogspot.com Reviews

https://baergblog.blogspot.com

Friday, April 23, 2010. Hooke's law in component form. We start with Hooke's law for the strain tensor, and then substitute the E and nu. Material properties for K and mu. We see that there is still a compression term, now on the right, but not a pure shear term, and both terms contain both material constants. We mention here that nu. The shear modulus is about is about 40 % of the Young's modulus. The bulk modulus (of compression) is therefore about 1.5 to 2 times larger than the shear modulus. The shea...

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Easy Elasticity Theory: Hooke's law in component form

http://baergblog.blogspot.com/2010/04/hookes-law-in-component-form.html

Friday, April 23, 2010. Hooke's law in component form. We start with Hooke's law for the strain tensor, and then substitute the E and nu. Material properties for K and mu. We see that there is still a compression term, now on the right, but not a pure shear term, and both terms contain both material constants. We mention here that nu. The shear modulus is about is about 40 % of the Young's modulus. The bulk modulus (of compression) is therefore about 1.5 to 2 times larger than the shear modulus. The shea...

2

Easy Elasticity Theory: March 2010

http://baergblog.blogspot.com/2010_03_01_archive.html

Thursday, March 25, 2010. In an earlier blog, the one with the example of stretched rubber tubing, we included a description of the concept of strain. Now, we try to make it more plausible, more precise, and to include shearing, as well as normal strain. We'll start with the one-dimensional case again. We choose a fixed coordinate system, and consider a surface somewhere inside a material body, at a point x =. In the x direction be u(x). Next, consider a point at a distance a. Is the first derivative of u.

3

Easy Elasticity Theory

http://baergblog.blogspot.com/2010/04/in-last-blog-we-saw-that-two-material.html

Wednesday, April 21, 2010. In the last blog, we saw that two material constants are required to describe elastic behavior in solids - the shear modulus G. And the modulus of compression K,. Which is also called the bulk modulus. Timoshenko and Goodier use the letter G. For the shear modulus, while Landau and Lifshitz use the Greek letter mu). Have about the same value. Times the trace of the strain tensor. Inverting this and substituting in Hooke's law,. Subscribe to: Post Comments (Atom). Relative volum...

4

Easy Elasticity Theory: Compression (or extension) of a rod

http://baergblog.blogspot.com/2010/04/compression-or-extension-of-rod.html

Thursday, April 22, 2010. Compression (or extension) of a rod. Consider a rod with a rectangular cross section, so that Cartesian coordinates can be used in 3 dimensions. Let the longer dimension of the rod be along the z. Axis, with a compressive force per unit area f. Applied to both ends. Imagine that the rod is thick enough that it won't bend under the applied force. By the same argument, the force on any plane perpendicular to the x- or y- axes must be zero. Plane through the rod is equal to f,.

5

Easy Elasticity Theory: Hooke's Law

http://baergblog.blogspot.com/2010/04/hookes-law.html

Tuesday, April 20, 2010. In order to combine the shear and compression terms into one expression for Hooke's law, Landau and Lifshitz make use of the Kronecker delta symbol. For the compression term, this is straightforward:. If i = j, the delta symbol is equal to one, and we have the expression given for compression in the previous blog. For the shear term, we need to subtract the trace components from the strain tensor, leaving only the off-diagonal shear components:. Subscribe to: Post Comments (Atom).

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baergblog.blogspot.com

Easy Elasticity Theory

Friday, April 23, 2010. Hooke's law in component form. We start with Hooke's law for the strain tensor, and then substitute the E and nu. Material properties for K and mu. We see that there is still a compression term, now on the right, but not a pure shear term, and both terms contain both material constants. We mention here that nu. The shear modulus is about is about 40 % of the Young's modulus. The bulk modulus (of compression) is therefore about 1.5 to 2 times larger than the shear modulus. The shea...

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