When a piezoelectric material is subjected to a quasi-static electric (or mechanical) load, part of the input energy is converted to the mechanical (or electric) domain. The piezoelectric coupling factor k2 is defined as the ratio between the converted energy and the supplied energy. This factor is often considered as a measure of the transduction efficiency of the material. Another definition of the coupling factor is a non-dimensional ratio of material coefficients. To examine the compatibility between these two different definitions, we consider several quasi-static loading cycles of a simple one-dimensional problem. We show that in some specific cases, the two definitions are equivalent, but that in other cases they are incompatible. In addition, we show that in specific quasi-static loading cycles, the converted energy may be increased by a slight modification of the unloading part of the cycle.

中文翻译：

---

压电耦合因子的模糊定义

当压电材料承受准静态电（或机械）载荷时，部分输入能量转换为机械（或电）域。压电耦合系数 k2 被定义为转换能量与供给能量之比。该因素通常被认为是衡量材料转导效率的指标。耦合因子的另一个定义是材料系数的无量纲比。为了检查这两种不同定义之间的兼容性，我们考虑了一个简单的一维问题的几个准静态加载循环。我们表明，在某些特定情况下，这两个定义是等效的，但在其他情况下它们是不兼容的。此外，我们表明，在特定的准静态加载循环中，