Problem 2775. Rule of mixtures (composites) - lower bound

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=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>Ef: elastic modulus of the fiber material</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>Em: elastic modulus of the matrix material</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>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>Write a function to calculate this bound for various values.</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

37 Solutions
30 Solvers

Last Solution submitted on Oct 01, 2021

Last 200 Solutions

Problem Comments

Problem Recent Solvers30

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 2775. Rule of mixtures (composites) - lower bound

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers30

Suggested Problems

More from this Author139

Problem Tags

Community Treasure Hunt

Problem 2775. Rule of mixtures (composites) - lower bound

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers30

Suggested Problems

More from this Author139

Problem Tags

Community Treasure Hunt

Players