General Continuum Mechanics
In this book, a new approach is pioneered in providing a unified theory in continuum mechanics. General Continuum Mechanics is intended for the beginner, but it develops advanced material covering interdisciplinary subjects. With applications of convective, Lagrangian, and Eulerian coordinates and the first and second laws of thermodynamics, the first-year graduate student will learn solid mechanics and fluid mechanics as an integrated subject. Electromagnetic continuum and relativistic continuum are included. The conservational properties of mass, momentum, and energy on earth and in the universe constitute the ingredients of this book. They are the monumental contributions of Newton, Maxwell, and Einstein, a panorama of beauty of universal laws that evolved over the last four centuries. No boundaries are needed to separate them, but rather we integrate them in harmony and place them in perspective. This is the book for interdisciplinary studies to carry out the modern scientific projects in which engineering, physics, and applied mathematics must be combined.
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boundary conditions boundary layer Chap Christoffel symbols conservation form conservation of mass consider constant constitutive equations continuum mechanics contravariant convective coordinate system coordinate transformations covariant derivative curvature curvilinear coordinates deﬁned deformed density deviatoric differential equation discussed displacement Dt Dt dx dy elastic entropy equations of motion Eulerian coordinates ﬁrst law ﬂow fluid ﬂuid mechanics function given by Eq governing equations gradients incompressible integral invariant isotropic kinematic Lagrangian coordinates law of thermodynamics linear material metric tensor momentum equation Newtonian nonlinear normal Note obtain particle physical plane plastic principal strain rate-of-deformation tensor relation relativistic represents respectively rotation scalar Section shear strain shear stresses shown in Fig solid mechanics solution spacetime strain tensor stress tensor Subsection Substituting Eq symmetric tangent vectors temperature theory three-dimensional turbulence undeformed variables velocity view of Eqs viscoelastic viscous vorticity wave yield surface