The chapter provides an overview of the development and significance of the non-linear field theories of mechanics, as detailed in the book *The Non-Linear Field Theories of Mechanics* by Clifford Truesdell and Walter Noll. The book, originally published in 1965, is a comprehensive treatise on the subject, emphasizing the reorganization of classical mechanics and the simplification of complex concepts. Truesdell and Noll aimed to make continuum mechanics "simple, easy, and beautiful," using abstract linear algebra and direct notation to present the material in a clear and geometrically illuminating manner.
The chapter highlights the contributions of Truesdell and Noll to the field, including their work on constitutive equations, material behavior, elasticity, and fluidity. It also discusses the subsequent developments in continuum mechanics, such as the extension of representation theorems, the axiomatic foundation of mechanics by Noll, and the treatment of internal constraints and constitutive restrictions in nonlinear elasticity.
The preface to the third edition, written by Stuart S. Antman, reflects on the impact of the book and the subsequent research in the field. It notes the continued relevance of Truesdell and Noll's work, particularly in areas like coexistent phases, thermodynamics, and materials with memory. The chapter concludes by acknowledging the slow but steady progress in advancing the scientific conquests laid out in the book, emphasizing the foundational role it has played in the field.The chapter provides an overview of the development and significance of the non-linear field theories of mechanics, as detailed in the book *The Non-Linear Field Theories of Mechanics* by Clifford Truesdell and Walter Noll. The book, originally published in 1965, is a comprehensive treatise on the subject, emphasizing the reorganization of classical mechanics and the simplification of complex concepts. Truesdell and Noll aimed to make continuum mechanics "simple, easy, and beautiful," using abstract linear algebra and direct notation to present the material in a clear and geometrically illuminating manner.
The chapter highlights the contributions of Truesdell and Noll to the field, including their work on constitutive equations, material behavior, elasticity, and fluidity. It also discusses the subsequent developments in continuum mechanics, such as the extension of representation theorems, the axiomatic foundation of mechanics by Noll, and the treatment of internal constraints and constitutive restrictions in nonlinear elasticity.
The preface to the third edition, written by Stuart S. Antman, reflects on the impact of the book and the subsequent research in the field. It notes the continued relevance of Truesdell and Noll's work, particularly in areas like coexistent phases, thermodynamics, and materials with memory. The chapter concludes by acknowledging the slow but steady progress in advancing the scientific conquests laid out in the book, emphasizing the foundational role it has played in the field.