Continuum Mechanics for Engineers

Abstract

t is fitting to start this, the preface to our second edition, by thanking all of those who used the text over the last six years. Thanks also to those of you who have inquired about this revised and expanded version. We hope that you find this edition as helpful as the first to introduce seniors or graduate students to continuum mechanics. The second edition, like its predecessor, is an outgrowth of teaching continuum mechanics to first- or second-year graduate students. Since my father is now fully retired, the course is being taught to students whose final degree will most likely be a Masters at Kettering University. A substantial percentage of these students are working in industry, or have worked in industry, when they take this class. Because of this, the course has to provide the students with the fundamentals of continuum mechanics and demonstrate its applications. Very often, students are interested in using sophisticated simulation programs that use nonlinear kinematics and a variety of constitutive relationships. Additions to the second edition have been made with these needs in mind. A student who masters its contents should have the mechanics foundation necessary to be a skilled user of today’s advanced design tools such as nonlinear, explicit finite elements. Of course, students need to augment the mechanics foundation provided herein with rigorous finite element training. Major highlights of the second edition include two new chapters, as well as significant expansion of two other chapters. First, Chapter Five, Fundamental Laws and Equations, was expanded to add material regarding constitutive equation development. This includes material on the second law of thermodynamics and invariance with respect to restrictions on constitutive equations. The first edition applications chapter covering elasticity and fluids has been split into two separate chapters. Elasticity coverage has been expanded by adding sections on Airy stress functions, torsion of noncircular cross sections, and three-dimensional solutions. A chapter on nonlinear elasticity has been added to give students a molecular and phenomenological introduction to rubber-like materials. Finally, a chapter introducing students to linear viscoelasticity is given since many important modern polymer