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Internally Constrained Mixtures of Elastic Continua

A treatment of internally constrained mixtures of elastic continua at a common temperature is developed. Internal constraints involving the deformation gradient tensors and the common mixture temperature are represented by a constraint manifold, and an internally constrained mixture of elastic continua is associated with each unique equivalence class of unconstrained mixtures. The example of intrinsic incompressibility of each constituent first proposed by Mills is discussed.