Introduction to the Variational Formulation in Mechanics

Part IIVariational Formulations in Mechanics

The goal of the second part of this book is to introduce the reader to the foundations and developments of variational formulations in the field of mechanics. To do this, Chapter 3 is devoted to the basic underlying ingredients that play a major role in variational formalism. This way of approaching the modeling of a physical phenomenon is called the Method of Virtual Power. From the basic kinematical setting, going through the mathematical duality and reaching the so‐called Principle of Virtual Power, this variational structure provides a clear and elegant framework to unambiguously understand the interplay between model kinematical hypotheses and the way they shape the realm of forces and stresses. This establishes direct consequences in terms of governing equations, boundary conditions, jump conditions, and constitutive modeling, among others.

The modeling of the mechanics of deformable bodies in the most general scenario is addressed in Chapter 3. In addition, classical kinematical constraints considered over the bodies are discussed in detail, as well as issues related to different observational descriptions of the phenomena, namely Eulerian and Lagrangian descriptions, and their application in different specific problems. Chapters 4, 5 and 6 present the application of variational formulations in classical problems of mechanics in the infinitesimal strain regime, including hyperelastic behavior and its different formulations, ...