A cube of linear elastic material is again subjected to a vertical compressive stress s1 in the 1-direction, but is now constrai
ned (ε ¼0) in both the 2 and the 3 directions. (a) Findexpressionsfortheinducedtransversestresses, s2 and s3 intermsof s1. Hence, derive an expression for the ‘effective modulus’ (s1/ε1) in this case. (b) Sketch the variation of effective modulus with n, and comment on the limiting values when n¼0 (foam) and n z 0.5 (rubber). (c) Explain why the rubber soles of running shoes are designed with some combination of air or gel pockets, partially foamed rubber, and a tread
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