Navier-Cauchy Equations

The set of linear elasticity partial differential equations that relate the displacement field of a homogeneous, isotropic, linear‑elastic continuum to internal stresses and applied body forces; in the static isotropic case they are commonly written with Lamé constants λ and μ as μ ∇^2 u + (λ + μ) ∇(∇·u) + b = 0, where u is the displacement field and b the body force per unit volume.