Problem 2778. Rule of mixtures (composites) - lower and upper bounds (volumes)

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>Sometimes, the volume fraction is not known and must be calculated from known volumes (Vf and Vm). In this case, ff = Vf / (Vf + Vm).</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 either bound, depending on which bound is requested in the input string and using the known volumes.</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

102 Solutions
23 Solvers

Last Solution submitted on Jul 26, 2021

Last 200 Solutions

Problem Recent Solvers23

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 2778. Rule of mixtures (composites) - lower and upper bounds (volumes)

Solution Stats

Last 200 Solutions

Problem Recent Solvers23

Suggested Problems

More from this Author139

Problem Tags

Community Treasure Hunt

Problem 2778. Rule of mixtures (composites) - lower and upper bounds (volumes)

Solution Stats

Last 200 Solutions

Problem Recent Solvers23

Suggested Problems

More from this Author139

Problem Tags

Community Treasure Hunt

Players