Author | Rakotomanana, L. R. author |
---|---|
Title | A Geometric Approach to Thermomechanics of Dissipating Continua [electronic resource] / by L. R. Rakotomanana |
Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2004 |
Connect to | http://dx.doi.org/10.1007/978-0-8176-8132-6 |
Descript | XV, 265 p. online resource |
Geometry and Kinematics -- 2.1 Introduction to continuum motion -- 2.2 Geometry of continuum -- 2.3 Discontinuity of fields on continuum -- 2.4 Deformation of continuum -- 2.5 Kinematics of continuum -- Conservation Laws -- 3.1 Introduction -- 3.2 Boundary actions and Cauchyโs theorem -- 3.3 Conservation laws -- Continuum with Singularity -- 4.1 Introduction -- 4.2 Continuum with singularity of the rate type -- 4.3 Operators on continuum with singularity -- 4.4 General equations of continuum -- Thermoviscous Fluids -- 5.1 Fluids without singularity distribution -- 5.2 Fluids with singularity distribution -- 5.3 Overview of fluid-like models -- Thermoviscous Solids -- 6.1 Solids without singularity distribution -- 6.2 Solids with singularity distribution -- 6.3 Intermediate configurations -- 6.4 Overview of solid-like models -- 6.5 Elastic waves in nonclassical solids -- Solids with Dry Microcracks -- 7.1 Geometry -- 7.2 Kinematics -- 7.3 Conservation laws -- 7.4 Constitutive laws at the crack interface -- 7.5 Concluding remarks -- Conclusion -- A Mathematical Preliminaries -- A.1 Vectors and tensors -- A.1.1 Vector, space, basis -- A.1.2 Linear maps and dual vector spaces -- A.1.3 Tensors, tensor product -- A.2 Topological spaces -- A.2.1 Topological spaces -- A.2.2 Continuous maps -- A.2.3 Compactness -- A.2.4 Connectedness -- A.2.5 Homeomorphisms and topological invariance -- A.3 Manifolds -- A.3.1 Definition of manifold -- A.3.2 Tangent vector -- A.3.3 Tangent dual vector -- A.3.5 Mappings between manifolds -- B Invariance Group and Physical Laws -- B.1 Conservation laws and invariance group -- B.1.1 Newton spacetime -- B.1.2 Leibniz spacetime -- B.1.3 Galilean spacetime -- B.1.4 Physical roots of conservation laws -- B.2 Constitutive laws and invariance group -- B.2.1 Spacetime of Cartan -- B.2.2 Objectivity (frame indifference) of constitutive laws -- C Affinely Connected Manifolds -- C.1 Riemannian manifolds -- C.1.1 Metric tensor -- C.2 Affine connection -- C.2.1 Metric connection, Levi-Civita connection -- C.2.2 Affine connections -- C.2.3 Covariant derivative of tensor fields -- C.3 Curvature and torsion -- C.3.1 Lie-Jacobi bracket of two vector fields -- C.3.2 Exterior derivative -- C.3.3 Poincarรฉ Lemma -- C.3.4 Torsion and curvature -- C.3.5 Holonomy group -- C.4.1 Orientation on connected manifolds -- C.4.4 Stokesโ theorem -- C.5 Brief history of connection -- D Bianchi Identities -- D.1 Skew symmetry -- D.2 First identities of Bianchi -- D.3 Second identities of Bianchi -- E Theorem of Cauchy-Weyl -- E.1 Theorem of Cauchy (1850) -- E.2 Theorem of Cauchy-Weyl (1939) -- References