Energy Equilibrium and Newton CG Method

This lecture covers topics related to continuum mechanics, including reference and deformed configurations, deformation gradient, energy density function, elastic energy, strain, stress, linear elasticity, hyperelastic materials, St. Venant-Kirchhoff model, Corotated linear elasticity, Neo-Hookean model, force balance in 3D solids, Lamé parameters, equilibrium conditions, isotropic linear elasticity, surface traction, force balance, divergence of a vector field, divergence theorem, finite element discretization, energy minimization, Newton's method, conjugate gradients, iterative linear systems solver, gradient descent, conjugacy, conjugate direction method, conjugate gradient method, line search Newton-CG method, and outlook on implementing Newton CG for elastic equilibrium solve.