Fung-a First Course In Continuum Mechanics.pdf -

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.

Scope and audience

Introductory graduate/advanced undergraduate textbook. Assumes knowledge of calculus, differential equations, and basic vector calculus; minimal tensor background required. Covers kinematics, stress and equilibrium, constitutive relations, elasticity (linear and some nonlinear aspects), and basic fluid mechanics perspectives.

Structure and main topics

Kinematics of deformation

Material (Lagrangian) and spatial (Eulerian) descriptions. Displacement, deformation gradient F, right and left Cauchy–Green tensors (C = FᵀF, B = FFᵀ). Measures of strain: Green–Lagrange strain E and small-strain tensor ε for infinitesimal deformations. Polar decomposition F = R U = V R and interpretation (rotation + stretch).

Balance laws and stress measures

Conservation of mass. Equilibrium and momentum balance in integral and differential forms. Stress tensors: Cauchy stress σ (true stress), first and second Piola–Kirchhoff stresses (P, S) and their relations via F and J = det F. Traction vector t = σ·n and traction theorem.

Constitutive relations

Principles guiding constitutive modeling: objectivity, material symmetry, and thermodynamic restrictions. Linear elasticity: Hooke’s law in tensor form, generalized elastic moduli, isotropic elasticity with Lamé constants (λ, μ) and relations to Young’s modulus E and Poisson’s ratio ν. Simple nonlinear constitutive models overview (hyperelasticity, strain energy functions). Fung-a first course in continuum mechanics.pdf

Small-deformation elasticity

Governing equations: equilibrium ∇·σ + b = 0 with linearized strain ε = (∇u + ∇uᵀ)/2. Boundary-value problems and common solutions: uniaxial tension, shear, torsion of rods, bending of beams (with continuum perspective). Stress concentration, compatibility conditions, and uniqueness theorems.