Multiaxial constitutive laws for ferroelectric ceramics that include hysteresis, rate dependence, saturation, and are capable of simulating nonproportional loading are needed for stress analysis and reliable design of smart structures. The relationship between constitutive behavior of ferroelectric ceramics and phenomena that occur across multiple length scales is reviewed. A framework for the development of phenomenological constitutive laws at the macroscopic scale is presented, and a multiaxial law with 900 (70.5 and 109.5 when rhombohedral) and 1800 switching effects is described.
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