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(1) We consider the case of a beam or plate splits along its nlid- plane where the total height is 2h, the
length of the crack is a, the overall length of the beam is L, and the out-of?plane depth is b, as shown in
Figure 1. The material is assumed to be isotropic, homogeneous and linear elastic,with E = ... 

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P top h Mode I a L P bottom h Mode I a P. P h Mode II h a FIGURE 1. Analysis of fracture in composite
beam/plate by linear superposition.

 

 

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(2) Show that the enthalpy per unit mass of a linear elastic isotropic materials can be expressed as 1 +
Us h(oij, s) = - OkkOkk +00 1 - Es Oijij E Poco Okk (S - So)+ 2co (s - so) tho NO where the various terms
are defined as discussed in the lecture.

 

 

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(3) A thin metallic wire deposited onto a flexible substrate such as PDMS, can be treated as a beam on
an elastic foundation. Standard beam theory can be used to address such problems by treating the
distributed force q(3:) to be a function of the amount of displacement into the substrate; s...