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* [[Constitutive equations]]. For elastic materials, [[Hooke's law]] represents the material behavior and relates the unknown stresses and strains. The general equation for Hooke's law is <math display="block"> \boldsymbol{\sigma} = \mathsf{C}:\boldsymbol{\varepsilon},</math>
where <math>\boldsymbol{\sigma}</math> is the [[Cauchy stress tensor]], <math>\boldsymbol{\varepsilon}</math> is the [[infinitesimal strain]] tensor, <math>\mathbf{u}</math> is the [[Displacement (vector)|displacement vector]], <math>\mathsf{C}</math> is the fourth-order [[stiffness tensor]], <math>\mathbf{F}</math> is the body force per unit volume, <math>\rho</math> is the mass density, <math>\boldsymbol{\nabla}</math> represents the [[nabla operator]], <math>(\bullet)^\mathrm{T}</math> represents a [[transpose]], <math>\ddot{(\bullet)}</math> represents the second [[material derivative]] with respect to time, and <math>\mathsf{A}:\mathsf{B} = A_{ij}B_{ij}</math> is the inner product of two second-order tensors (summation over repeated indices is implied).
=== Cartesian coordinate form ===
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