Continuum mechanics studies the foundations of deformable body mechanics from a mathematical perspective. It also acts as a base upon which other applied areas such as solid mechanics and fluid mechanics are developed. This book discusses some important topics, which have come into prominence in the latter half of the twentieth century, such as material symmetry, frame-indifference and thermomechanics. The study begins with the necessary mathematical background in the form of an introduction to tensor analysis followed by a discussion on kinematics, which deals with purely geometrical notions such as strain and rate of deformation. Moving on to derivation of the governing equations, the book also presents applications in the areas of linear and nonlinear elasticity. In addition, the volume also provides a mathematical explanation to the axioms and laws of deformable body mechanics, and its various applications in the field of solid mechanics.
Fluid mechanics is the study of fluids including liquids, gases and plasmas and the forces acting on them. Its study is critical in predicting rainfall, ocean currents, reducing drag on cars and aeroplanes, and design of engines. The subject is also interesting from a mathematical perspective due to the nonlinear nature of its equations. For example, the topic of turbulence has been a subject of interest to both mathematicians and engineers: to the former because of its mathematically complex nature and to the latter group because of its ubiquitous presence in real-life applications. This book is a follow-up to the first volume and discusses the concepts of fluid mechanics in detail. The book gives an in-depth summary of the governing equations and their engineering related applications. It also comprehensively discusses the fundamental theories related to kinematics and governing equations, hydrostatics, surface waves and ideal fluid flow, followed by their applications.
