Fundamentals of Continuum Mechanics

Continuum mechanics is a mathematical framework for studying the transmission of force through and deformation of materials of all types. The goal is to construct a framework that is free of special assumptions about the type of material, the size of deformations, the geometry of the problem, etc. Of course, no real materials are actually continuous; nevertheless, treating material as continuous is a great advantage since it makes possible the use of mathematical tools of continuous functions, such as differentiation. In addition to being convenient, this approach works remarkably well. This is true even at size scales for which the justification of treating the material as a continuum might be debatable. The ultimate justification is that predictions made using continuum mechanics are in accord with observations and measurements. Fundamentals of Continuum Mechanics comprehensively introduces the subject and the background for formulation of numerical methods for large deformations and a wide range of material behaviours. It provides the foundations for further study, not just of these subjects, but also for formulations of more complex material behaviour and their implementation computationally. It is divided into five parts, covering mathematical preliminaries, stress, motion and deformation, balance of mass, momentum and energy, and ideal constitutive relations Key features: A concise introductory course text on continuum mechanics Covers the fundamentals of continuum mechanics Uses modern tensor notation Contains problems and accompanied by a companion website hosting solutions Fundamentals of Continuum Mechanics is an ideal textbook for introductory graduate courses for students in mechanical and civil engineering, as well as those studying material science, geology and geophysics and biomechanics. It is also a concise reference for industry practitioners.

John W. Rudnicki received his bachelor, masters and PhD degrees from Brown University, the last in 1977. He has been on the faculty of Northwestern University since 1981, where he is now Professor of Civil and Environmental Engineering and Mechanical Engineering. He is a Fellow of the American Society of Mechanical Engineers. He has been awarded the Biot Medal from the American Society of Civil Engineers, the Brown Engineering Alumni Medal, the Daniel C. Drucker Medal from the American Society of Mechanical Engineers and the Engineering Science Medal from the Society of Engineering Science. His research has been primarily in geomechanics, specifically the inelastic behavior and failure of geomaterials. He has been especially interested in deformation instabilities in brittle rocks and granular media, including their interactions with pore fluids, with applications to the mechanics of earthquakes and environment– and resource–related geomechanics.