We present a conservative method for the interaction between an inviscid compressible flow and a fragmenting structure. On the fluid side, we consider an inviscid Euler fluid in conservative form discretized using a Finite Volume method combining Lax-Friedrichs fluxes in fluid cells located near the opening fractures when the density and pressure are zero or very low with high-order monotonicity-preserving fluxes elsewhere. On the solid side, we consider a fragmenting solid discretized with a Discrete Element method where fragmentation owns through the breaking of links between the particles discretizing the solid. The fluid-solid coupling is achieved by an Immersed Boundary technique through the modification of the Finite Volume fluxes in the vicinity of the solid. A time explicit approach is used for the computation of the energy and momentum transfer between the solid and the fluid.