Problem 2776. Rule of mixtures (composites) - lower and upper bounds

Created by goc3

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>The</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://en.wikipedia.org/wiki/Rule_of_mixtures\"><w:r><w:t>rule of mixtures</w:t></w:r></w:hyperlink><w:r><w:t> is used in the mechanical design of composite structures to estimate the elastic modulus (Ec) based on the following properties:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[    Ef: elastic modulus of the fiber material\n    Em: elastic modulus of the matrix material\n    ff or fm: volume fraction of the fiber or matrix material (ff = 1 – fm)]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Based on these values, the lower-bound estimate of elastic modulus is calculated by:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Ec = 1 / (ff / Ef + (1 – ff) / Em).</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>On the other hand, the upper-bound (linear) estimate of elastic modulus is calculated by:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Ec = ff * Ef + (1 – ff) * Em.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Write a function to calculate both bounds for various values. Also, return the difference between the modulus estimates and the ratios of this difference to both moduli estimates.</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Solve

Solution Stats

39 Solutions
26 Solvers

Last Solution submitted on Apr 03, 2022

Last 200 Solutions

Problem Comments

Problem Recent Solvers26

Problem Tags

composites fiber materials materials science matrix mechanical design volume fraction

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 2776. Rule of mixtures (composites) - lower and upper bounds

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers26

Suggested Problems

More from this Author139

Problem Tags

Community Treasure Hunt

Problem 2776. Rule of mixtures (composites) - lower and upper bounds

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers26

Suggested Problems

More from this Author139

Problem Tags

Community Treasure Hunt

Players