Multi-scale Modelling: Homogenisation Introduction
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Questions and Answers

What is the purpose of the Mean Field Method in predicting the behavior of heterogeneous materials?

  • To provide accurate predictions
  • To estimate the density of the materials
  • To analyze the chemical composition of the materials
  • To give an efficient way of prediction, though not entirely accurate (correct)

    • In the context of elasticity, what do Voigt and Reuss estimates represent?

  • Material properties under different loading directions
  • Isostrain and Isostress conditions (correct)
  • Stiffness values of isotropic materials
  • Different types of composites

    • What do Voigt and Reuss estimates assume regarding the conditions among the phases?

  • Isotropy in all phases
  • Isostrain and Isostress conditions, respectively (correct)
  • No interaction between the different phases
  • Equal stiffness in all phases

    • How does the Mean Field Method handle the prediction of behavior in heterogeneous materials compared to other methods?

    <p>It offers an efficient way of prediction, though not entirely accurate</p> Signup and view all the answers

    In the context of composite materials, what is the role of a shape factor in representing interactions between matrix and inclusions?

    <p>Representing the spherical nature of inclusions</p> Signup and view all the answers

    Why are Voigt and Reuss estimates considered simple mean-field schemes?

    <p>For assuming isostrain and isostress conditions among phases</p> Signup and view all the answers

    What is the primary aim of homogenisation in computational engineering?

    <p>To determine effective macroscopic properties</p> Signup and view all the answers

    Why do heterogeneities in a material cause high frequency oscillations in the solution?

    <p>Due to the material's inner structure</p> Signup and view all the answers

    What key role does the Representative Volume Element (RVE) play in homogenisation?

    <p>Calculating average stress and strain</p> Signup and view all the answers

    Which mathematical concept is used to connect the interior of the RVE with its boundaries in homogenisation?

    <p>Divergence Theory</p> Signup and view all the answers

    In homogenisation, what do we aim to obtain about a heterogeneous material?

    <p>Effective macroscopic properties</p> Signup and view all the answers

    How does direct numerical study typically handle the behavior of heterogenous materials?

    <p>By ignoring high frequency oscillations</p> Signup and view all the answers

    What concept does Eshelby's work on elastic ellipsoidal inclusions address?

    <p>Deformation of inclusions within a matrix</p> Signup and view all the answers

    Which operation involves 'cutting out' the inclusion to allow it to deform freely?

    <p>Eigenstrain application</p> Signup and view all the answers

    In Eshelby's work, what happens during the 'Inclusion Reinsertion' operation?

    <p>A compensating stress is applied to restore the inclusion to its original shape</p> Signup and view all the answers

    Which material has the highest tensile strength among the ones listed?

    <p>Carbon Fibre</p> Signup and view all the answers

    What property do Modulus and Tensile strength measure in materials?

    <p>Elasticity</p> Signup and view all the answers

    In which direction are strength and stiffness generally much higher for composite materials?

    <p>Along the fiber direction (isostrain)</p> Signup and view all the answers

    According to Reuss estimation, what is the relationship between Composite Load (Pc), Matrix Load (Pm), and Fiber Load (Pf)?

    <p>Pc = Pm + Pf</p> Signup and view all the answers

    What is Voigt's estimation known as?

    <p>Isostrain</p> Signup and view all the answers

    Which of the following equations represents Composite Elongation (∆Lc) in the direction of loading correctly?

    <p>$∆Lc = ∆Lm + ∆Lf$</p> Signup and view all the answers

    What does Voigt's estimation state about the load carried by the composite?

    <p>It is equal to the sum of Matrix Load and Fiber Load</p> Signup and view all the answers

    According to the extreme conditions stated, what do Isostrain and Isostress represent in composite materials?

    <p>Extreme conditions for strength and stiffness</p> Signup and view all the answers

    In homogenisation, what does the effective behavior define?

    <p>The behavior of a heterogeneous material at a macroscopic level</p> Signup and view all the answers

    What method is used to solve the field equations for deriving the localization tensor in homogenisation?

    <p>Green's function methods</p> Signup and view all the answers

    What does the local perturbation in the strain field represent in homogenisation?

    <p>Fourth-rank localisation tensor</p> Signup and view all the answers

    When applying boundary conditions in RVE, what are we trying to understand?

    <p>How the RVE behaves as part of a larger structure</p> Signup and view all the answers

    What is the primary purpose of replacing coefficient tensor A(y) by effective homogenous coefficients in homogenisation?

    <p>To make the system computationally cheaper</p> Signup and view all the answers

    Does the effective behavior ( ext{𝐂𝐂 𝐞𝐞𝐞𝐞𝐞𝐞}) depend on the length of RVE and boundary conditions?

    <p>Yes, it depends on both</p> Signup and view all the answers

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