Analysis of Plane Stress and Plane Strain using Cartesian coordinates and the Stress Function Method (Airy stress functions). 3. Advanced Material Models

While Part I usually covers the basics—stress, strain, and linear elasticity— dives into the "large deformation" theory. This is where the math gets serious. Instead of assuming materials only deform slightly (like a steel beam), Part II looks at materials that can stretch and twist significantly, such as rubber or biological tissues. Key Topics Covered

Since Part II emphasizes 3D stress states and energy methods, model the example problems in a simple Python script (using NumPy for tensor math) or an FEA tool like CalculiX or Ansys Student. Seeing the numerical solution validates the analytical solution.

4.1 Lame’s equations for axisymmetric stress 4.2 Compound cylinders and shrink fits 4.3 Rotating disks of uniform and variable thickness 4.4 Autofrettage of thick cylinders

6.1 Strain energy and complementary energy 6.2 Castigliano’s first and second theorems 6.3 Unit load method (virtual work) 6.4 Principle of minimum potential energy 6.5 Rayleigh-Ritz method for approximate solutions

Part II focuses on , moving from the foundational concepts in Part I to more complex analytical applications. You can access the full collection and specific chapters through the official University of Auckland portal . Key Content in Solid Mechanics Part II