| | | Gonzalez & Stuart's Modern Text (Cambridge) | | --- | --- | --- | | Primary Editions | 1st (1969), 2nd (1977), 3rd (1994) | 1st (2008) | | Target Audience | Engineers, physical & biological scientists | Applied mathematicians & engineers | | Style & Emphasis | Problem formulation, physical intuition, derivations of governing equations for applications | Unified derivation of balance laws (e.g., isothermal and thermal theories) | | Learning Aids | Chapter problems; supplementary notes and problem solutions are available for earlier editions | Extensive exercises with fully worked solutions to odd-numbered questions; a complete solutions manual is available to instructors | | Prerequisites | Not explicitly stated, but assumes standard engineering mathematics background | Basic linear algebra and differential equations |
| Chapter | Title | |:---|:---| | 1 | Tensor algebra | | 2 | Tensor calculus | | 3 | Continuum mass and force concepts | | 4 | Kinematics | | 5 | Balance laws | | 6 | Isothermal fluid mechanics | | 7 | Isothermal solid mechanics | | 8 | Thermal fluid mechanics | | 9 | Thermal solid mechanics |
In addition, continuum mechanics has numerous applications in physics, including the study of the behavior of fluids and solids under extreme conditions, such as high temperatures and pressures. In biology, continuum mechanics is used to understand the behavior of living tissues, such as blood vessels and muscles. Fung-a first course in continuum mechanics.pdf
| Chapter | Title | |:---|:---| | 1 | The Concept of Continua | | 2 | Vectors and Tensors | | 3 | Stress | | 4 | Principal Stresses and Principal Axes | | 5 | Analysis of Deformation | | 6 | Velocity Fields and Compatibility Conditions | | 7 | Constitutive Equations | | 8 | Isotropy | | 9 | Mechanical Properties of Fluids and Solids |
The mathematical framework of nonlinear elasticity is based on the following fundamental equations: | | | Gonzalez & Stuart's Modern Text
Nonlinear elasticity is a branch of continuum mechanics that deals with the study of materials that exhibit a nonlinear relationship between stress and strain. Nonlinear elastic materials can exhibit a variety of behaviors, including:
| Feature | Fung, A First Course in Continuum Mechanics | Gonzalez & Stuart, A First Course in Continuum Mechanics | | :--- | :--- | :--- | | | Bioengineering, Biomechanics, Aeroelasticity | Mathematics, Applied Mathematics | | Target Audience | Engineers, advanced undergraduates & grads | Applied mathematicians, advanced undergrads & grads | | Approach | Physical, problem formulation-based | Rigorous mathematical, self-contained | | Coverage | Broad, includes thermal theories | Broad, but focuses heavily on fluids & linear elasticity | | Prerequisites | Basic linear algebra & ODEs | Basic linear algebra & multivariate calculus | Nonlinear elastic materials can exhibit a variety of
Fung presumes a standard undergraduate engineering or science background. The key requirements are:
Both editions of Fung's book share a logical structure: starting from fundamental mathematics, then building up the core physical concepts of stress and deformation, before applying them to real materials.
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