Chess but the pieces get bigger when they eat other pieces

Here's a dilemma that's been puzzling me for a while. Say you're in the middle of a heated game of chess, with pieces having been killed left and right, their dead bodies littering the battlefield. But they're not littering the battlefield. The battlefield, in fact, is as clean as it was on move one, without a dead body in sight. Where are the dead pieces?

Most chess players use the terms "captured" or "taken", implying that the pieces were loaded into a van and trucked off to some prisoner-of-war camp somewhere. But be realistic — a chess board doesn't have enough room for vans to weave in between pieces, and neither kingdom seems to have a permanent territory anywhere. It seems to me like there's only one plausible explanation for where these pieces are going: they are being eaten by the pieces that capture them.

But if that's the case, why doesn't each chess piece double in size after eating an entire other piece of its size? Well, that's because most chess pieces are made of rigid, solid material and physically cannot grow. They're not built to scale. But mine are. The full power of chess pieces can finally be unleashed.