Balance laws and a dissipation inequality for general constituents undergoing disarrangements and mixing

Multiphase structured deformations provide a multiscale geometrical setting suitable for distinguishing among (1) separate constituents – N bodies that occupy mutually disjoint regions in space at all times and that submacroscopically may form voids or undergo slips, (2) intermingling constituents – N bodies, each of which splits into small non‐overlapping cells that may be in contact with cells of the same or of different constitutents, and (3) mixing constituents – N bodies that interpentrate by occupying overlapping regions in space. Earlier research based on multiphase structured deformations has established balance laws and a dissipation inequality for each constituent within the mixture when that constituent is an elastic body. The balance laws and dissipation inequality were obtained via a limiting argument from corresponding relations for intermingling constitutents whose motions approximate those of the mixing constituents. Here, such limiting arguments are shown to provide balance laws and a dissipation inequality for a much broader class of constituents.