A nearly incompressible rubber block is confined between

Question

A nearly incompressible rubber block is confined between two frictionless rigid walls as shown in the figure. When uniform pressure P is applied to the right end, the length of the block is changed by x₁ = (1 - α)X₁. When α = 0.1,

(a) calculate the value of the strain energy density and

(b) the magnitude of applied pressure P on the right end.

Assume a plane-strain problem and use a Mooney-Rivlin material with A₁₀ = 80 MPa, A₀₁ = 20 MPa, and K = 1,000 MPa.