In the past the rational mechanics of deformable media was largely concerned with materials governed by linear constitutive equations. In recent years, the theory has expanded considerably towards covering materials for which the constitutive equations are inherently nonlinear, and/or whose mechanical properties resemble in some respects those of a fluid and in others those of a solid. In the present article we formulate a satisfactory global mathematical theory of moving deformable media, which includes all these aspects.
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