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It is shown that realistic material response allows for three qualitatively different types of behavior for inflation of incompressible elastic hollow spheres and stretched cylinders. The pressure may increase monotonically, or it may increase and then decrease, or it may increase, decrease, and then increase again. A simple condition on the material response curve for uniaxial compressive stress is used to classify materials with respect to spherical inflation and to examine which type of behavior will occur for a particular material and initial geometry. Similar results are obtained for inflation of axially stretched hollow cylinders. The results are also applicable to elastic-plastic strain hardening materials.

Pressure maximum behavior in inflation of incompressible elastic hollow spheres and cylinders