Most parts of the Earth are made of multi-phase materials. The physical mechanisms of deformation of a multi-phase material differ from those of a homogeneous material in several ways. A key issue here is how the rate of deformation (or the strength of a polycrystalline material) is related to those of individual materials (or crystals) and their volume fraction, orientation and geometry. Experimental observations and theoretical models of the deformation of a multi-phase material are reviewed. It is shown that the plastic deformation of a multi-phase material is controlled not only by the rheological contrast (the contrast in effective viscosity) and the volume fraction of each phase but also by the stress–strain distribution that depends on the geometry of each phase. The case of partial melt deserves special attention. Mechanical contrast is large in this case and as a consequence the properties of a partial melt depend strongly on the fraction and geometry of the melt. Principles that determine the geometry of melt in a partially molten material are discussed.

Key words Reuss average (model), Voigt average (model), Hill average (model), Hoff's analogy, Taylor average (model), Sachs average (model), variational principle, self-consistent approach, percolation, partial melt, dihedral angle.