A method and arrangement for producing a three-dimensional material composite using an expansion body includes at least two metal bodies having surface regions resting loosely against one another. The composite is heated to a target temperature and the surface regions are pressed against one another so that an integral connection is established. At least one expansion cavity having a predefined initial volume is arranged in one of the metal bodies or in an additional expansion body resting against one of the metal bodies in such a manner that when the expansion cavity expands, the surface regions to be connected are pressed against one another. A predefined quantity of at least one substance which is gaseous at least at a target temperature is hermetically enclosed in the expansion cavity before the target temperature is reached.