Continuum mechanics and thermodynamics [Elektronisk resurs] from fundamental concepts to governing equations.

• Cover; Continuum Mechanics and Thermodynamics; Title; Copyright; Contents; Preface; Acknowledgments; Notation; 1 Introduction; Part I Theory; 2 Scalars, vectors and tensors; 2.1 Frames of reference and Newton's laws; 2.2 Tensor notation; 2.2.1 Direct versus indicial notation; 2.2.2 Summation and dummy indices; 2.2.3 Free indices; 2.2.4 Matrix notation; 2.2.5 Kronecker delta; 2.2.6 Permutation symbol; 2.3 What is a tensor?; 2.3.1 Vector spaces and the inner product and norm; Finite-dimensional spaces and basis vectors; Proof; Multilinear functions; Euclidean space; Inner product and norm. 
• 2.3.2 Coordinate systems and their basesEuclidean point space; Coordinate systems; Orthonormal basis and Cartesian coordinates; Nonorthogonal bases and covariant and contravariant components; 2.3.3 Cross product; 2.3.4 Change of basis; Properties of Q; Proof; 2.3.5 Vector component transformation; 2.3.6 Generalization to higher-order tensors; 2.3.7 Tensor component transformation; Proving a quantity is a tensor; Proof; 2.4 Tensor operations; 2.4.1 Addition; 2.4.2 Magnification; 2.4.3 Transpose; 2.4.4 Tensor products; 2.4.5 Contraction; Contracted multiplication; Scalar contraction; Proof. 
• 2.4.6 Tensor basisProof; 2.5 Properties of tensors; 2.5.1 Orthogonal tensors; 2.5.2 Symmetric and antisymmetric tensors; Proof; 2.5.3 Principal values and directions; Proof; 2.5.4 Cayley-Hamilton theorem; Proof; 2.5.5 The quadratic form of symmetric second-order tensors; Proof; 2.5.6 Isotropic tensors; Proof; 2.6 Tensor fields; 2.6.1 Partial differentiation of a tensor field; 2.6.2 Differential operators in Cartesian coordinates; Gradient; Curl; Divergence; Laplacian; 2.6.3 Differential operators in curvilinear coordinates; Polar cylindrical coordinates; Spherical coordinates. 
• 2.6.4 Divergence theoremExercises; 3 Kinematics of deformation; 3.1 The continuum particle; 3.2 The deformation mapping; 3.3 Material and spatial field descriptions; 3.3.1 Material and spatial tensor fields; 3.3.2 Differentiation with respect to position; 3.4 Description of local deformation; 3.4.1 Deformation gradient; Proof; 3.4.2 Volume changes; 3.4.3 Area changes; 3.4.4 Pull-back and push-forward operations; 3.4.5 Polar decomposition theorem; Proof; 3.4.6 Deformation measures and their physical significance; 3.4.7 Spatial strain tensor; 3.5 Linearized kinematics; 3.6 Kinematic rates. 
• 3.6.1 Material time derivative3.6.2 Rate of change of local deformation measures; Rate of deformation and spin tensors; Rate of change of stretch; Eigenvalues and eigenvectors of the rate of deformation tensor d; Rate of change of strain; Rate of change of volume; Rate of change of oriented area; 3.6.3 Reynolds transport theorem; Exercises; 4 Mechanical conservation and balance laws; 4.1 Conservation of mass; 4.1.1 Reynolds transport theorem for extensive properties; 4.2 Balance of linear momentum; 4.2.1 Newton's second law for a system of particles. 
• 4.2.2 Balance of linear momentum for a continuum system. 

• Treats subjects directly related to nonlinear materials modeling for graduate students and researchers in physics, materials science, chemistry and engineering. 

Ämnesord

Kontinuumsmekanik  (sao)

Termodynamik  (sao)

Continuum mechanics. 

Thermodynamics -- Mathematics. 

Thermodynamics  (LCSH)

Continuum mechanics  (LCSH)

Genre

Electronic books.  (LCSH)

Klassifikation

QA808.2 .T33 2012 (LCC)

531 (DDC)

Ucb (kssb/8 (machine generated))