Use brass jacketed FMJ bullets. We are talking .380 acp here.
Expanding bullets in a .380 acp would have to have extremely thin jackets and extremely soft, pure, unalloyed lead. They would also need more "power" behind them than you normally find inside of a 380 acp casing, in order to work well. You are not talking much in the way of pressure or energy or power at all in general when you talk about a round like the .380 acp. Still, it has it's proven place in the line of cartridges engineered for personal defense.
While shooting JHP .380 acp into old phone books may be interesting in the way of an "experiment" that shows good expansion, you have to keep in mind that the human body is far from being constructed like a telephone book. The human body is not a block of gelatin, either. There are some things to consider here.
You have to get the bullet through clothing. You have to get through varying thickness of skin, underwhich is first found certificial muscle tissue of varying thickness, hydration and density. Then there is varying degrees of thickness, hydration and density in fat and cartilage. then you have varying degrees of thickness, hydration and density in standard muscle tissue. under that you begin to reach bones of varying densities and thicknesses. It is not until your bullet makes it through all of those layers that you will even begin to find nerve clusters, and important internal organs. You have a lot of material to shoot through to get to the vitals that will "shut down" your attacker. A JHP will hinder that process in a round such as the .380 acp. It will stop in the outer layers of the body and maybe not reach a vital point inside of the body.
When dealing with low pressures and low power, you need to concentrate your efforts on getting that projectile deep inside of the body cavity. A JHP in a round like .380 ACP will hinder that process. You need to go for the deep penetration instead. Consider that an unexpanded FMJ .380 slug arriving inside of the body cavity and striking a major internal organ will shut down your attacker. It does not have to expand to do that. It simply needs to arrive deep inside of the body. A quick-expander lodged in certificial muscle tissue will not shut down an attacker. In fact it might cause him adrenalin surges while his body is still mechanically intact to carry out the attack on your person with more vitality than at the outset of the attack.
Get the hardest most solid FMJ for your .380 acp you can find and stick with it. Use brass jacketed FMJ over the copper, because the brass ones are harder and likely to penetrate deeper. Copper is softer than brass and it will distort a little bit on impact. That could reduce penetration.
.380 acp is a very deadly cartridge when used correctly. Guns made for it are opften very concealable. They are small but they have a reasonable sized bore diameter. They throw a reasonably sized projectile. But none of that means anything unless you can get that projectile into the body cavity where it can contact vitals.
Use brass FMJ for defensive rounds. Use a good quality handgun as well. Expanding bullets in a low-pressure round may not be a good idea at all in a cartridge like this one.
