Fung-a First Course In Continuum Mechanics.pdf [verified] May 2026

This is a solid content outline for a study guide, summary, or video series based on "A First Course in Continuum Mechanics" by Y.C. Fung. Since Fung’s book is known for its rigorous, biomechanics-flavored approach to tensors and nonlinear elasticity, this content is designed to be concept-first, notation-heavy (addressing his unique style), and application-aware (linking to soft tissues and blood flow).

Article: Fung — A First Course in Continuum Mechanics

Overview

A First Course in Continuum Mechanics by Y. C. Fung is a concise, widely used introduction to continuum mechanics aimed at advanced undergraduates and beginning graduate students in engineering and applied mechanics. The book emphasizes physical intuition, clear derivations, and practical applications in solid and fluid mechanics. This article summarizes the book’s scope, core concepts, pedagogical approach, key equations, typical applications, strengths, limitations, and suggested reading paths. Fung-a first course in continuum mechanics.pdf

Conclusion

Part 3: Stress (The Force Inside)

3.1 Cauchy Stress Tensor ($\sigma_ij$ or $\mathbfT$) This is a solid content outline for a

  1. Linear elasticity: Linear elasticity describes the behavior of a medium that returns to its original shape after the removal of external forces.
  2. Non-linear elasticity: Non-linear elasticity describes the behavior of a medium that exhibits non-linear stress-strain relationships.
  3. Viscoelasticity: Viscoelasticity describes the behavior of a medium that exhibits both elastic and viscous behavior.