## Theory of Composites Modeled by Interpenetrating Solid ContinuaThe differential equations and boundary conditions describing the behavior of a finitely deformable, heat conducting composite material are derived by means of a systematic application of the laws of continuum mechanics to a well-defined macroscopic model consisting of interpenetrating solid continua. Each continuum represents one identifiable constituent of the N- constituent composite. The influence of viscous dissipation is included in the general treatment. Although the motion of the combined composite continuum may be arbitrarily large, the relative displacement of the individual constituents is required to be infinitesimal in order that the composite not rupture. The linear version of the equations in the absence of heat conduction and viscosity is exhibited in detail for the case of the two-constituent composite. The linear equations are written for both the isotropic and transversely isotropic material symmetries. For the linear isotropic equations both static and dynamic potential representations are obtained, each of which is shown to be complete. |

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### Contents

THEORY | 8 |

Boundary Conditions | 44 |

General Equations and Boundary Conditions | 50 |

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angular momentum antisymmetric antisymmetric matrix antisymmetric tensors assumed body forces boundary conditions chain rule coefficients combined continuum concentrated force constants constituents composite material constitutive equations defined deformation differential equations dissipation divergence theorem elastic equations and boundary equations of motion everything vanishes Fiber Reinforced Composite Fibers Figure H.F. TIersten heat conducting integral forms intermediate configuration interpenetrating solid continua invariant isotropic composite material jump conditions law of thermodynamics linear homogeneous equations mass density material coordinates matrix and fibers matrix material n-constituents numerical solutions obtain orthogonal orthogonal group Piola-KIrchhoff Piola-KIrchhoff stress tensor plane waves propagating principle of material Reinforced Composite Body Rensselaer Polytechnic Institute respectively satisfy Schematic Diagram Section small field variables small fields superposed static stress tensor surface of discontinuity surface tractions Surface Waves Propagating symmetric theory thickness vibration three constituents composite three continua tion transversely isotropic composites variational principle wave equations written x^-axis x^-direction yields nontrivial solutions