Initially unpoled soft PZT was subjected to a proportional, coaxial electromechanical loading. The ratio of compressive stress to electric field was changed between the experiments. From this series of nonlinear polarization and strain responses were obtained. Based on an offset method, initial domain switching states in the two-dimensional stress-electric field space were determined. In continuum mechanics, thin walled tubes are used to investigate multi-axial stress states. In this context, thin walled means a ratio of wall thickness to radius of 1:10 or thinner. However, simple linear dielectric analysis indicates an inhomogeneous electric field distribution in such geometries.
Therefore, the suitability of hollow cylinders (in the range from thick to thin walled tubes) for multi-axial electromechanical experiments has to be investigated. Simulations with a finite element tool based on a phenomenological constitutive model for ferroelectric and ferroelastic hysteresis behavior were performed. The results confirm inhomogeneous distributions of electric fields and stresses after poling. A geometry variation is discussed to minimize these effects.