Abstract
We derive a nonlinear theory of heat-conducting micropolar mixtures in Lagrangian description. The kinematics, balance laws, and constitutive equations are examined and utilized to develop a nonlinear theory for binary mixtures of micropolar thermoelastic solids. The initial boundary value problem is formulated. Then, the theory is linearized and a uniqueness result is established.
Highlights
The importance of the study of mixtures was recognized long ago when the basic concepts of the theory have been established and the possible applications of the mathematical models have been identified
The theoretical progress in the field is discussed in detail in review articles by Bowen [10], Atkin and Craine [11, 12], Bedford and Drumheller [13], and in the books of Samohyl [14] and Rajagopal and Tao [15]
The quantities TK(αL), MK(αL), ᏼK, KL, Υ, η, and QK must be prescribed by constitutive equations
Summary
The importance of the study of mixtures was recognized long ago when the basic concepts of the theory have been established and the possible applications of the mathematical models have been identified. The motion of a mixture of two continua is described by two equations, x = x(X,t) and y = y(Y,t), and the particles X and Y are assumed to occupy the same position at current time t, so that x = y. In contrast to mixtures of fluids, the theory on mixtures of solids is developed naturally in the Lagrangian description and it leads to different results. In this case, the motion of a binary mixture is described by the equations x = x(X,t) and y = y(Y,t), where the particles under consideration occupy the same position in the reference configuration, so that X = Y
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