Continuum Mechanics in the Earth Sciences, by William I. Newman

The continuum hypothesis furnishes a framework in which the discreet nature of matter at the microscopic scale is abandoned at the macroscopic scale and the medium is dealt with as a continuum. In this framework, field variables represent continuous functions of space and time and the governing equations are described using a set of partial differential equations. Furthermore, field variables are not associated any more with particles, rather they represent the average behaviour of an enormous number of particles contained within a representative averaging volume. This necessitates that new forces and fluxes are defined that do not appear at the microscopic level. As an example, the interaction of different material bodies at the continuum description suggests that two different kinds of forces appear; namely body forces and surface forces. The later required careful investigation and has been hypothesised to be a function of both the position and orientation of the surface. The continuum mechanics covers wide range of applications including solid mechanics, fluid mechanics, etc. It is therefore diverse in the large number of phenomena, and it encounters based on the set of governing laws that are essentially of the same origin. Therefore, to cover all interesting topics pertinent to the different applications are rather cumbersome and require large volume text. However, the current book by William Newman succeeded in such difficult job by focusing on the main essence of the topic leaving the very fine details to more specialised text books. As the book describes the continuum hypothesis as applied to Earth sciences, topics particulars to these systems have been highlighted. This includes deformation of Earths materials, flow of complex classical and geophysical fluid systems, dimensional analysis, a survey on numerical methods are among the topics covered in this book.