A cubic elastomer is compressed by a steel piston in a deformable mold placed on a...

 

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A cubic elastomer is compressed by a steel piston in a deformable mold placed on a steel table, as shown in the figure below. The mold is initially cubic, tightly fitting with the elastomer block. The mold will expand along lateral directions under the inner pressure, P. It can be assumed that the relationship between the size of the mold and the pressure is linear: a = ao + B-P, where ao is the initial mold size and B is a system constant. Assume that the lateral surfaces remain planar during deformation. Derive, in the framework of rubber elasticity, the relationship between the piston pressure (P) and the piston displacement, d. Clearly state all your assumptions. Steel piston -Elastomer block ao -Deformable mold Steel table A cubic elastomer is compressed by a steel piston in a deformable mold placed on a steel table, as shown in the figure below. The mold is initially cubic, tightly fitting with the elastomer block. The mold will expand along lateral directions under the inner pressure, P. It can be assumed that the relationship between the size of the mold and the pressure is linear: a = ao + B-P, where ao is the initial mold size and B is a system constant. Assume that the lateral surfaces remain planar during deformation. Derive, in the framework of rubber elasticity, the relationship between the piston pressure (P) and the piston displacement, d. Clearly state all your assumptions. Steel piston -Elastomer block ao -Deformable mold Steel table

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