Whatever the model you may be trying to work out; there may come the time when you may, possibly, want to compare it with the classic Heckel model: R. W. Heckel, "Density-pressure relationships in powder compaction", Transactions of the Metallurgical Society of the AIME, Vol. 221, August 1961, 671-675.

There are a lot of compaction equations which differ in interpretation of their coeficients. Selection of applied equation depend on your ppwder material system and depend on required descriptor of the results. Is your powder ceramic (rigid) metallic (able to plastic deformation) or polimeric (extrem elastic and plastic deformation)? You can find some starting overview here: Panelli R., Filho A.R.: A study of a new phenomenological compacting equation, Powder Technology 114 2001 255–261

https://www.ipen.br/biblioteca/2001/07391.pdf.

or some comparison of metalic, ceramic and polymeric systems: https://www.epma.com/world-pm2010-proceedings/422-world-pm2010-powder-pressing/file

critical comparison of heckel and Kawakita equations is here: https://doi.org/10.1016/S0032-5910(02)00111-0

or relatively new contribution of G. Aryanpour: https://doi.org/10.1016/j.powtec.2015.02.032

For Hot isostatic pressing you can use the Norton Green model of compaction :

DOI: 10.1002/adem.201600348

For cold compaction you have as an example CamClay or Drucker Prager Cap model.

DOI: 10.1016/j.ijsolstr.2007.11.021

Best