2.1 - Taylor’s expansion
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Practice Questions
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What does residual stress refer to in materials?
💡 Hint: Think about what happens to stress when loads are not applied.
How many independent components does the stiffness tensor have after major symmetry?
💡 Hint: Start with 81 and apply the symmetries we discussed.
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Interactive Quizzes
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What is the main purpose of the stress-strain relation?
💡 Hint: Think about why engineers care about material properties.
True or False: Residual stress refers to the stress present when a material is under an external load.
💡 Hint: Consider the definition we've discussed.
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Challenge Problems
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If a material's behavior deviates significantly from linearity under certain load conditions, how would this affect the application of Taylor's expansion? Provide a detailed argument.
💡 Hint: Consider the implications of large deformations and how they might impact dependency relations.
How would you apply Taylor's expansion in a scenario where you have a composite material and different properties for its constituents? Describe your approach.
💡 Hint: Think about how the properties interact and consolidate results using rules for composites.
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