A cylindrical slug that has a diameter of 1 in. and is 1 in. high is placed at the center of a 2-in.-diameter cavity in a rigid die. The slug is surrounded by a compressible matrix, the pressure of which is given by the relation
Pm = 40,000 ˆ†V/Vom psi,
Where m denotes the matrix and Vom is the original volume of the compressible matrix. Both the slug and the matrix are being compressed by a piston and without any friction. The initial pressure on the matrix is zero, and the slug material has the true stress-true strain curve of
σ = 15,000e04.

Obtain an expression for the force F versus piston travel d up to d = 0.5 in.

o O 1" 2" Compressible_ matrix