## Constitutive Equations for Anisotropic and Isotropic MaterialsConstitutive equations define the response of materials which are subjected to applied fields. This volume presents the procedures for generating constitutive equations describing the response of crystals, isotropic and transversely isotropic materials. The book discusses the application of group representation theory, Young symmetry operators and generating functions to the determination of the general form of constitutive equations. Basic quantity tables, character tables, irreducible representation tables and direct product tables are included. |

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### Contents

1 | |

15 | |

Chapter III ELEMENTS OF INVARIANT THEORY | 43 |

Chapter IV INVARIANT TENSORS | 53 |

Chapter V GROUP AVERAGING METHODS | 109 |

Chapter VI ANISOTROPIC CONSTITUTIVE EQUATIONS AND SCHURS LEMMA | 133 |

THE CRYSTALLOGRAPHIC GROUPS | 159 |

CONTINUOUS GROUPS | 201 |

THE CUBIC CRYSTALLOGRAPHIC GROUPS | 265 |

Chapter X IRREDUCIBLE POLYNOMIAL CONSTITUTIVE EXPRESSIONS | 297 |

327 | |

333 | |

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### Common terms and phrases

absolute vector Basic Quantities basis for functions carrier space Cartesian coordinate system character table column vector constitutive equation constitutive expressions crystal class crystallographic groups decomposition deﬁned defines the transformation entries ﬁrst form the carrier given group R3 independent components inequivalent irreducible representations integrity basis invariant under R3 invariants of degree invariants of symmetry irreducible expression isomers linear combinations linearly independent functions linearly independent invariants matrix products matrix representation monomial terms number of linearly obtained orthogonal group permutations polynomial functions problem of determining procedure product table property tensors quantities of type redundant terms reference frames Rivlin scalar-valued functions second-order tensor-valued functions sets of invariants sets of tensors skew-symmetric second-order tensors Smith summation symmetric group symmetric second-order tensors symmetrized Kronecker symmetry class symmetry type n1...np syzygies tensors of symmetry Theorem three-dimensional transformation properties types F1 typical multilinear elements xgxg Young symmetry operators