The only way you can get access to the remanent strain (as far as I am concerned) is by measuring the virgin loop. Since you only measure displacements any loop you measure after the virgin one will retrace the displacement of the previous loop (we neglect here fatigue etc) and you cannot accesed the remanent value again. In general, this value will greatly depend on your extrinsic contributions (meaning domains). Any variable that changes extrinsic contributions  such as defects can affect it. However, there is not a priori a 1 to one 1 correlation between them. For instance, if you cool faster your sample the stresses created during this process should modify also this value.

In general d33* is an empirical quantification used to normalized strains with the purpose on getting to know one important paramter of ferroelectrics for actautors applications. Therefore, from my point of view, one should report the value of a retrasable loop (not virgin) unless stated so (for technological purposes at least). This would mean you have to substract your remanent strain or in other words the zero of your second loop corresponds to the repeatable displacement. Hope it helps!

I understand that you want to measure d33* values for fields larger than the coercive field Ec? So, in the range, where you can rather be forgotten with an approximate linearity of d33(E).

Do I understand you correctly?

Indeed, normally d33* is defined just as the ratio between strain and field as a normalized paramter in analogy to small signal properties, but most generally it is reported in the field range where non-linearity is present.

The origin of the remnant strain depends on the material you studied, whether it is a ferroelectric material or a relaxor material, and the testing condition as it is the first loop applie to the fresh sample or the following circles.

@Matias: This paper is found very helpful, J. Electroceramics (2012) 29: 71-93

thanks

I would like to thank Dr. Wawrzala and Dr. Zhao for participating this discussion.

thank you both of you.

Regards,

Supratim