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Manufacturers of crunchy munchies such as cheese crisps use compression testing machines to gauge product quality. The crisp, or whatever, is placed between opposing plates, which then move together. As the crisp is crunched, the force is measured as a function of the distance that the plates have moved. The output of the compression testing machine is a graph of force versus distance that is much like Figure 1.3. What aspects of the graph might be measures of product quality? Model the test as a row of tiny balloons between parallel plates. Each single balloon might follow a force-distance behavior of the form σ = Ke(1 - q(e)), where σ is the force, K is Young's modulus, e is strain or distance, and q(e) is a function that measures departures from Hooke's law, to allow for soggy crisps. Each balloon obeys this relationship up until the random strain at which it bursts. Determine the mean force as a function of strain. Use F(x) for the cumulative distribution function of failure strain.
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