In this paper we establish a nonlinear theory of binary mixtures of elastic solids with microstructure. The independent constitutive variables are the displacement fields, displacement gradients, microdeformation tensors and their gradients. The basic equations are derived in Lagrangian description. The theory is linearized and a uniqueness theorem with no definiteness assumption on the constitutive coefficients is presented. The theory is used to study a special kind of microstructure in which the microdeformation tensor is isotropic. The problem of a concentrated body moment is investigated.
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