Repeat problem 41 with the specimen of size \(100 \times 100 \times 10 \mathrm{~mm}^{3}\) and the dimensions of the cavity \(104 \times 104 \times 9 \mathrm{~mm}^{3}\). Elastic constants of the plastic are: \(E=10 \mathrm{GPa}, v=0.3\).

Problem 42:

A rectangular plastic specimen of size \(100 \times 100 \times 10 \mathrm{~mm}^{3}\) is placed in a rectangular metal cavity. The dimensions of the cavity are \(101 \times 101 \times 9 \mathrm{~mm}^{3}\). The plastic is compressed by a rigid punch until it is completely inside the cavity. Due to Poisson effect, the plastic also expands in the \(x\) and \(y\) direction and fill the cavity. Calculate all stress and strain components and the force exerted by the punch. Assume there is no friction between all contacting surfaces. The metal cavity is rigid. Elastic constants of the plastic are: \(E=10\) \(\mathrm{GPa}, v=0.3\).

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Rigid punch Plastic Rigid punch Plastic Rigid die Rigid die