UCI ENGRMAE 150 - SolutionQuiz3 (2 pages)

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SolutionQuiz3



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SolutionQuiz3

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Pages:
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School:
University of California, Irvine
Course:
Engrmae 150 - Mechanics of Strctr
Mechanics of Strctr Documents
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CBEMS155 MAE156 FAM Quiz 3 Solution Given Non isotropic cubic crystal Bulk modulus 1 K VP V V V exx eyy ezz Required Prove K C11 2C12 3 Assumption Hydrostatic pressure Solution The structure is under hydrostatic pressure so xx yy zz P 1 For a non isotropic cubic crystal we have xx C11 exx C12 eyy ezz yy C11 eyy C12 exx ezz zz C11 ezz C12 exx eyy 2 Adding the three stress terms together we get xx yy zz C11 exx eyy ezz 2C12 exx eyy ezz 3P C11 V V 2C12 V V 3P C11 2C12 V V C11 2C12 V V P 3 Substitute the above expression into the bulk modulus definition we get 1 3 V V 1 K P P K V V C11 2C12 V V K 3 V V 4 so we get K C11 2C12 3 2 5


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