Publisher's Synopsis
Continuum Mechanics is a branch of physical mechanics that describes the macroscopic mechanical behavior of solid or fluid materials considered to be continuously distributed. It is fundamental to the fields of civil, mechanical, chemical and bioengineering. Continuity is expressed by the spatial and temporal continuity between the starting position of the car and its position at the considered instant. The Eulerian approach fixes cameras along the track and records which car passes which camera at which time. Any car has velocity, the outside world is immobile. The velocity of all cars at each instant defines the flow. Continuity is expressed in the differentiability in space and time, at any moment, of physical quantities. Both Lagrangian and Eulerian approaches yield mathematically the same result, but the Eulerian formulation is often found more practical. Describing the motion of a fluid through volume elements at fixed locations (any of the "cameras") in function of time is termed Eulerian to honour the Swiss mathematician Leonhard Euler who introduced this type of specification to study fluid motion and the mechanics (dynamics and kinematics) of deforming material. The mass of a continuum object is determined by multiplying its volume by its density. The concept of mass conservation is intuitively obvious for rigid-body translation or rotation: The object retains its shape, size, density, and volume. Therefore, the mass of the object remains constant from the initial to the final position and orientation. The same is easily conceived for volume-constant deformation, for example a cube deformed into a same-volume parallelepiped. The shape has changed but the amount of matter, hence mass, is same. Common deformation is a dynamic process that combines the change of shape, displacement and rotation. Continuum Mechanics and Thermodynamics discloses new ideas in continuum and quasi-continuum modeling of systems with a large number of degrees of freedom and sufficient complexity to require thermodynamic closure. Special emphasis is placed research studies seeking to bridge the gap between discrete and continuum approaches as well as micro and macro scales, by means of homogenization, statistical averaging, and other mathematical tools aimed at the judicial elimination of small time and length scales. In particular, the book focuses on simultaneous descriptions of complex systems at several disparate scales. This Book is intended to introduce junior and senior-level engineering students, as well as academics, to the basic principles of continuum mechanics and their applications to real engineering problems.
