Mechanics and Durability of Solids, Volume I

Intended for a first course in continuum mechanics and constitutive modeling at the senior undergraduate and the introductory graduate level, the focus of this book is on a unified "mechanistic" approach that uses energy concepts for modeling a large range of engineering material behavior. In the presentation, 1D-Think models lead to the development of various fundamentals of continuum mechanics, such as deformation and strain, momentum balance, stress and stress states, thermoelasticity and elasticity bounds, plasticity, and yield design. Along these lines, the bases for a common language among core disciplines in engineering sciences are developed, in a mathematical, yet eloquent manner. The textbook evolved from lecture notes of a one-semester course developed by the authors at the Massachusetts Institute of Technology, as well as in France, Germany, and Brazil. Key Features of the Book *Parts I and II introduce the two pillars of continuum mechanics, strain and stresses, with a focus on geometrical and physical interpretation, starting with the finite deformation theory. *Part III is dedicated to non-dissipative material behavior, with a focus on thermoelasticity and variational methods in elasticity, as well as to its application in heterogeneous material systems. *Part IV starts with 1D-plasticity, introducing ideal plasticity, hardening plasticity, and associated energy transformations. It is within the energy approach that the 1D-Think models are extended to 3D, introducing the notion of associated and non-associated plasticity. Finally, the concept of plastic collapse is introduced, leading to the development of the upper- and lower-bound theorems of limit analysis, which form the basis of modern yield design for engineering structures and material systems. *The mathematical developments in each chapter are illustrated through a set of accompanying blackboard exercises of the subject matter, a Training Set for recitation, followed by a broad spectrum of worked exercises suitable for homework, classroom assignments, quizzes, or take-home examinations.

Table of Contents:
I. DEFORMATION AND STRAIN. 1. Description of Finite Deformation. 2. Infinitesimal Deformation. II. MOMENTUM BALANCE, STRESS AND STRESS STATES. 3. Momentum Balance and Stress. 4. Stress and Stress States. III. ELASTICITY AND ELASTICITY BOUNDS. 5. Thermoelasticity. 6. The Theorem of Virtual Work and Variational Methods in Elasticity. IV. PLASTICITY AND YIELD DESIGN. 7. 1D-Plasticity—An Energy Approach. 8. Plasticity Models. 9. Limit Analysis and Yield Design. Appendix A: Reading Volume 1. Index.