The crown jewel. You will derive the continuity equation, the Cauchy equation of motion ($\nabla \cdot \boldsymbol{\sigma} + \rho \mathbf{b} = \rho \dot{\mathbf{v}}$), and the energy equation.
This is where the magic happens. You will see how the same equations become Hooke's Law (solid) or Newton's Law of Viscosity (fluid) based purely on the constitutive assumptions. A Better Alternative to the Pirated PDF If you are struggling to find a clean, safe PDF of the 4th Edition, buy a used 3rd Edition. Continuum Mechanics For Engineers 4th Edition Pdf
The 3rd Edition (Mase & Mase) is available on AbeBooks or eBay for as little as $15 shipped. The page numbers changed, but the tensor derivations have not. You can then use a free online errata sheet to catch the updates. "Continuum Mechanics for Engineers, 4th Ed" is the best "first principles" book for engineers who need to use FEA or CFD professionally. Is the PDF out there? Yes. Is it worth the legal headache and security risk? Probably not. The crown jewel
You will likely find that you already paid for access through your tuition. You will see how the same equations become
Have you used this text for a course? Drop a comment below about which chapter you found the most challenging—I usually hear "Chapter 2: Tensors" wins that prize.
Cauchy’s stress principle. You will derive why stress is a tensor and how to find principal stresses without looking at a Mohr's circle.