Stress and Strain **Having some trouble getting going on (a and (b I should be able to finnish C&D with some initial help but just thought I'd include the whole problem. Thanks for all of your help in advance!**
A uniform block of material sits on a flat table. The material has density [Rho], bulk modulus [Mb] and shear modulus [Ms].The height of the block in absence of gravity is h. Choose gravity as pointing in the your coordinates so that gravity points in the -z direction.
(A) Calculate the stress and the strain throughout the block due to its own weight (i.e., provide a symbolic answer). Assume that the width and length of the block are much larger than the height so that the stress and strain are functions only of the z coordinate. (Hint: This problem is both easier and harder than it may seem. Use symmetry arguments concerning the form of the stress and strain tensors to simplify the problem. Yet also remember when attempting to find your answer, you do not know the actual height of the block since it deformed due to gravity (see also Part b below).)
(B) Calculate the change in height, [delta] h due to its own weight (i.e., provide a symbolic answer). Find an exact expression, and also an expression to first order in the material properties (i.e., density, etc). (C) Find two materials with substantially different combinations of density, bulk, and shear moduli (at room temperature, about 20\[Degree]
C). There are quite a few places to look on the Web. Possibilities are MatWeb, GoodFellow, ASM, Wikipedia and many more. (Manufactures that want to sell their materials are often good sources of material data since they want to make it easy for you to find what you are looking for.) Some places provide sear and Young's modulus instead of shear and bulk modulus, but you can use Taylor's Eq. 16.100 to translate between them. Also find the material properties for diamond. For each of the three materials make a table listing the material, its composition if applicable (e.g. for alloys), its density, and elastic constants (all three of them). Be sure to site your source of material, meaning website, literature, etc.
(D) Based on your calculation in part b), add to your table above the height change \[Delta]h of a block having a height of 1 m. Comment on your range of values, and how the materials you chose compared to diamond.