Micropolar lamination model for metal matrix composites undergoing thermoplastic deformation
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In the present paper we develop a micropolar thermoplasticity theory to model the bending and extensional deformation of metal matrix composites. In Part 2 we introduce the ply level geometry, notation and assumptions. It is shown that the assumption of ply level plane stress results in a symmetric stress tensor. In Part 3 the ply level constitutive equations are developed from the continuum thermodynamics of ``standard'' materials (Germain, Nguyen, Suquet, 1983). The stress, the moment, and the affinities are derived from the free energy function. The evolution of the internal state is obtained from a psuedo-potential of dissipation that is given in the space of affinities. The ply level micropolar tangent stiffness matrix is presented. In Part 4 we develop the micropolar lamination theory that relates ply level kinematics to laminate kinematics. The laminate level micropolar tangent stiffness matrix is given. In Part 5 it is demonstrated how the material constants in the ply-level constitutive equations may be derived from a micromechanics analysis.
